NCERT Solutions for Class 7 Maths Ganita Prakash Chapter 3 A Peek Beyond the Point

Page 47

1. Which scale helped you measure the length of the screws accurately? Why?
See SolutionThe scale with the smallest divisions (marked in tenths of a centimeter, which are millimeters) allowed for the most accurate measurement. This is because the ends of the screws did not align perfectly with the whole or half centimeter marks, requiring finer divisions to determine the length more precisely.

2.What is the meaning of 2 7/10 cm (the length of the first screw)?
See SolutionIt means the screw’s length is 2 whole centimeters plus 7 parts out of 10 equal divisions of the next centimeter (7/10 cm). In other words, it’s 2 centimeters and 7 tenths of a centimeter (or 2 centimeters and 7 millimeters).

3. Can you explain why the unit was divided into smaller parts to measure the screws?
See SolutionThe unit (centimeter) was divided into smaller parts (tenths, or millimeters) because the screws’ lengths were not exact whole numbers of centimeters. Smaller divisions are needed to measure lengths that fall between the whole number marks accurately.

4. Measure the following objects using a scale and write their measurements in centimeters (as shown earlier for the lengths of the screws): pen, sharpener, and any other object of your choice.
See SolutionPen Length: – 6 2/10 cm
Sharpener Length: 2 1/10 cm
Eraser length: 2 3/10 cm

5. Write the measurements of the objects shown in the picture.

See SolutionEraser length: 2 3/10 cm
Pencil length: 4 3/10 cm
Chalk length: 1 4/10 cm

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Arrange these lengths in increasing order:
(a) 9/10 (value 0.9)
(b) 1 7/10 (value 1.7)
(c) 130/10 (value 13.0)
(d) 13 1/10 (value 13.1)
(e) 10 5/10 (value 10.5)
(f) 7 6/10 (value 7.6)
(g) 6 7/10 (value 6.7)
(h) 4/10 (value 0.4)
See SolutionComparing the values: 0.4 < 0.9 < 1.7 < 6.7 < 7.6 < 10.5 < 13.0 < 13.1.
The lengths in increasing order are:
4/10, 9/10, 1 7/10, 6 7/10, 7 6/10, 10 5/10, 130/10, 13 1/10.

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1.  Arrange the following lengths in increasing order: 4 1/10, 4/10, 41/10, 41 1/10.
See SolutionConvert to decimals or common fractions to compare:
– 4 1/10 = 4.1
– 4/10 = 0.4
– 41/10 = 4.1
– 41 1/10 = 41.1
The values in increasing order are 0.4, 4.1, 4.1, 41.1.
The lengths in increasing order are: 4/10, 4 1/10 (which equals 41/10), 41 1/10.

2. Sonu is measuring some of his body parts. The length of Sonu’s lower arm is 2 7/10 units, and that of his upper arm is 3 6/10 units. What is the total length of his arm? (Three methods shown in text).
See SolutionWe need to calculate 2 7/10 + 3 6/10.
Method (a) Summing whole and fractional parts separately:
(2+3) + (7/10 + 6/10) = 5 + 13/10 = 5 + 1 3/10 = 6 3/10 units.
Method (b) Vertical addition (similar to Method a):
2 7/10
+ 3 6/10
——-
5 13/10 (which simplifies to 5 + 1 3/10 = 6 3/10)
Method (c) Converting to tenths:
2 7/10 = 27/10.
3 6/10 = 36/10.
Sum = 27/10 + 36/10 = (27+36)/10 = 63/10.
Converting back: 63/10 = 60/10 + 3/10 = 6 + 3/10 = 6 3/10 units.

Page 51

The lengths of the body parts of a honeybee are given. Find its total length.
Head: 2 3/10 units
Thorax: 5 4/10 units
Abdomen: 7 5/10 units
See SolutionTotal Length = Head + Thorax + Abdomen
Total Length = 2 3/10 + 5 4/10 + 7 5/10
Sum of whole parts = 2 + 5 + 7 = 14.
Sum of fractional parts = 3/10 + 4/10 + 5/10 = (3+4+5)/10 = 12/10.
Total = 14 + 12/10 = 14 + 1 2/10 = 15 2/10 units.

The length of Shylaja’s hand is 12 4/10 units, and her palm is 6 7/10 units, as shown in the picture. What is the length of the longest (middle) finger? (Assume finger length = hand length – palm length).
See SolutionWe need to calculate 12 4/10 – 6 7/10.
Method (a) shown in text:
(12-6) + (4/10 – 7/10)
= 6 + (-3/10)
= 6 – 3/10
= 5 + 1 – 3/10
= 5 + 10/10 – 3/10
= 5 + 7/10 = 5 7/10 units.
Method (b) shown in text (Vertical subtraction with borrowing):
12 4/10 becomes 11 14/10 (borrow 1 unit = 10 tenths)
– 6 7/10 stays – 6 7/10
——- ——-
5 7/10
The length of the finger is 5 7/10 units.

Discuss what is being done here and why.
See SolutionIn Method (b), we are subtracting 6 7/10 from 12 4/10. When looking at the tenths place, we cannot directly subtract 7/10 from 4/10 because 4 is less than 7.
So, we “borrow” 1 whole unit from the 12 units, leaving 11 units.
The borrowed 1 unit is converted into its equivalent in tenths, which is 10/10.
This is added to the existing 4/10, giving 10/10 + 4/10 = 14/10.
Now the subtraction becomes 11 14/10 – 6 7/10.
We can subtract the tenths: 14/10 – 7/10 = 7/10.
We can subtract the units: 11 – 6 = 5.
The result is 5 7/10. This regrouping (borrowing) allows subtraction when the fractional part of the first number is smaller than the fractional part of the second number.

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1. Try computing the difference 12 4/10 – 6 7/10 by converting both lengths to tenths.
See SolutionConvert to tenths:
12 4/10 = 120/10 + 4/10 = 124/10.
6 7/10 = 60/10 + 7/10 = 67/10.
Subtract:
124/10 – 67/10 = (124 – 67)/10 = 57/10.
Convert back to mixed number:
57/10 = 50/10 + 7/10 = 5 + 7/10 = 5 7/10 units.

2.  A Celestial Pearl Danio’s length is 2 4/10 cm, and the length of a Philippine Goby is 9/10 cm. What is the difference in their lengths?
See SolutionDifference = (Danio’s length) – (Goby’s length)
Difference = 2 4/10 – 9/10.
Convert 2 4/10 to tenths: 20/10 + 4/10 = 24/10.
Subtract: 24/10 – 9/10 = (24-9)/10 = 15/10.
Convert back: 15/10 = 10/10 + 5/10 = 1 + 5/10 = 1 5/10 cm (or 1.5 cm).

3. How big are these fish compared to your finger?
See SolutionThe Philippine Goby is 9/10 cm (or 0.9 cm) long. This is likely narrower and much shorter than an adult finger.
The Celestial Pearl Danio is 2 4/10 cm (or 2.4 cm) long. This might be slightly wider than an adult finger but is still much shorter than its length.

4. Observe the given sequences of numbers. Identify the change after each term and extend the pattern (write next 3 terms):
(a) 4, 4 3/10, 4 6/10, …
See SolutionChange is adding 3/10 (or 0.3). Next 3 terms: 4 9/10, 5 2/10, 5 5/10.
(b) 8 2/10, 8 7/10, 9 2/10, …
See SolutionChange is adding 5/10 (or 0.5). Next 3 terms: 9 7/10, 10 2/10, 10 7/10.
(c) 7 6/10, 8 7/10, 9 8/10, …
See SolutionChange is adding 1 1/10 (or 1.1). Next 3 terms: 10 9/10, 12, 13 1/10.
(d) 5 7/10, 5 3/10, 4 9/10, …
See SolutionChange is subtracting 4/10 (or 0.4). Next 3 terms: 4 5/10, 4 1/10, 3 7/10.
(e) 13 5/10, 13, 12 5/10, …
See SolutionChange is subtracting 5/10 (or 0.5). Next 3 terms: 12, 11 5/10, 11.
(f) 11 5/10, 10 4/10, 9 3/10, …
See SolutionChange is subtracting 1 1/10 (or 1.1). Next 3 terms: 8 2/10, 7 1/10, 6.

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What is the length of this smaller part?
See SolutionSince each one-tenth is split into 10 equal parts, the length of one smaller part is 1/10 of 1/10, which is 1/100 of a unit (one-hundredth).

How many such smaller parts make a unit length?
See SolutionThere are 10 tenths in a unit, and 10 hundredths in each tenth. So, there are 10 x 10 = 100 one-hundredth parts in a unit length.

What is the length of the folded paper?
See SolutionThe text states (and diagrams illustrate) that the folded length is 4 whole units, plus 4 tenths, plus 5 hundredths.
Length = 4 + 4/10 + 5/100.
This is read as “4 units and 4 one-tenths and 5 one-hundredths”.
(Note: Calculation shows half of 8 9/10 is 1/2 x 89/10 = 89/20 = 445/100 = 4 + 45/100 = 4 + 4/10 + 5/100).

How many one-hundredths make one-tenth? Can we also say that the length (of the folded paper) is 4 units and 45 one-hundredths?
See Solution– 10 one-hundredths (10/100) make one-tenth (1/10).
– Yes, the length 4 + 4/10 + 5/100 can also be expressed as 4 units and 45 one-hundredths (4 45/100). This is because 4/10 is equal to 40/100, so the total fractional part is 40/100 + 5/100 = 45/100.

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1. Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes.
See Solution(Note: Reading the exact points on the number line requires clear image interpretation. The answers below assume standard intervals based on context, but may need verification from the actual PDF image.)
– Box after 2/10 (which is 20/100): Likely 3/10 or 30/100.
– Box after 130/100: Likely 131/100 or 1 31/100.
– Box after 31/10: This is 3.1 or 3 10/100. The next box might be something like 3 15/100 or 3.15, but it depends on where the arrow points in the diagram.

2. Example (Wire measurement): The length 1 14/100 is shown written in three ways:
– “One and one-tenth and four-hundredths” ( 1 + 1/10 + 4/100 )
– “One and fourteen-hundredths” ( 1 14/100 )
– “One Hundred and Fourteen-hundredths” ( 114/100 )
Question: Can you see how they denote the same length?
See SolutionYes.
– 1 + 1/10 + 4/100 = 1 + 10/100 + 4/100 = 1 + 14/100 = 1 14/100.
– 1 14/100 = 100/100 + 14/100 = 114/100.
All three forms represent the same value.

3. For the lengths shown below (on rulers) write the measurements and read out the measures in words.
(Note: Precise measurements depend on interpreting the image scales. The answers below are based on likely readings).
– Ruler 1 (pointing between 5 7/10 and 5 8/10): Assuming it points to 5 78/100. Measurement: 5 78/100 units. Read: “Five and seventy-eight hundredths units”.
– Ruler 2 (pointing between 14 8/10 and 14 9/10): Assuming it points to 14 83/100. Measurement: 14 83/100 units. Read: “Fourteen and eighty-three hundredths units”.
– Ruler 3 (pointing between 7 and 7 1/10): Assuming it points to 7 2/100. Measurement: 7 2/100 units. Read: “Seven and two hundredths units”.
– Ruler 4 (pointing to 9 8/10): Measurement: 9 8/10 units (or 9 80/100). Read: “Nine and eight tenths units” (or “Nine and eighty hundredths units”).

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In each group, identify the longest and the shortest lengths. Mark each length on the scale. (Note: Marking on the scale requires drawing, which I cannot do, but I can identify the shortest and longest).

(a) 3/10, 3/100, 33/100
See SolutionValues: 3/10 = 0.30; 3/100 = 0.03; 33/100 = 0.33.
Comparing: 0.03 < 0.30 < 0.33.
Shortest: 3/100. Longest: 33/100.

(b) 3 1/10, 30/10, 1 3/10
See SolutionValues: 3 1/10 = 3.1; 30/10 = 3.0; 1 3/10 = 1.3.
Comparing: 1.3 < 3.0 < 3.1.
Shortest: 1 3/10. Longest: 3 1/10.

(c) 45/100, 54/100, 5/10, 4/10
See SolutionValues: 45/100 = 0.45; 54/100 = 0.54; 5/10 = 0.50; 4/10 = 0.40.
Comparing: 0.40 < 0.45 < 0.50 < 0.54.
Shortest: 4/10. Longest: 54/100.

(d) 3 6/10, 3 6/100, 3 6/10 6/100
See SolutionValues: 3 6/10 = 3.60; 3 6/100 = 3.06; 3 6/10 6/100 = 3 + 6/10 + 6/100 = 3 + 0.6 + 0.06 = 3.66.
Comparing: 3.06 < 3.60 < 3.66.
Shortest: 3 6/100. Longest: 3 6/10 6/100.

(e) 8/10 2/100, 9/100, 1 8/100
See SolutionValues: 8/10 + 2/100 = 0.80 + 0.02 = 0.82; 9/100 = 0.09; 1 8/100 = 1.08.
Comparing: 0.09 < 0.82 < 1.08.
Shortest: 9/100. Longest: 1 8/100.

(f) 7 3/10 5/100, 7 5/10, 7 41/100
See SolutionValues: 7 + 3/10 + 5/100 = 7 + 0.3 + 0.05 = 7.35; 7 5/10 = 7.50; 7 41/100 = 7.41.
Comparing: 7.35 < 7.41 < 7.50.
Shortest: 7 3/10 5/100. Longest: 7 5/10.

(g) 6 5/10 15/100 (assuming typo, perhaps 6 15/100 or 6 + 5/10 + 15/100 = 6.65? Let’s assume 6 15/100), 5 87/100, 5 7/100
See SolutionAssuming first number is 6 15/100 = 6.15. Other values: 5 87/100 = 5.87; 5 7/100 = 5.07.
Comparing: 5.07 < 5.87 < 6.15.
Shortest: 5 7/100. Longest: 6 15/100 (based on assumption).

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What will be the sum of 15 3/10 4/100 and 2 6/10 8/100? (Two methods shown in text).
See SolutionWe need to add 15 + 3/10 + 4/100 and 2 + 6/10 + 8/100.
Method 1 (Grouping Place Values):
Sum = (15+2) + (3/10+6/10) + (4/100+8/100)
= 17 + 9/10 + 12/100
= 17 + 9/10 + (10/100 + 2/100) (Regroup 12/100)
= 17 + 9/10 + 1/10 + 2/100 (Since 10/100 = 1/10)
= 17 + (9/10 + 1/10) + 2/100
= 17 + 10/10 + 2/100
= 17 + 1 + 2/100 (Since 10/10 = 1)
= 18 + 2/100 = 18 2/100.
Method 2 (Vertical Addition – similar logic):
15 3/10 4/100
+ 2 6/10 8/100
—————–
17 9/10 12/100 (Summing each place value)
= 17 10/10 2/100 (Regrouping 10 hundredths to 1 tenth)
= 18 2/100 (Regrouping 10 tenths to 1 unit)

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1. Are both these methods different? (Referring to Method 1 and Method 2 from the previous page for adding 15 3/10 4/100 + 2 6/10 8/100).
See SolutionNo, fundamentally both methods represent the same process. They both involve adding the corresponding place values (units, tenths, hundredths) together and then regrouping (or “carrying over”) whenever the sum in a place value reaches 10 or more. Method 2 (vertical addition) is just a more compact way of writing down the steps shown explicitly in Method 1.

Observe the addition done below for 483+268. Do you see any similarities between the methods shown above (for adding numbers with tenths/hundredths)?
Calculation shown:
(400+80+3)+(200+60+8)
= (400+200)+(80+60)+(3+8)
= 600+140+11
= 600+(100+40)+(10+1)
= (600+100)+(40+10)+1
= 700+50+1 = 751.
See SolutionYes, there are strong similarities. The addition of whole numbers shown here explicitly breaks down the numbers by place value (hundreds, tens, ones) and adds corresponding places together. When a sum in a place value is 10 or more (like 11 ones or 14 tens), it is regrouped into the next higher place value (11 ones -> 1 ten + 1 one; 14 tens -> 1 hundred + 4 tens). This is exactly analogous to the regrouping done when adding numbers with tenths and hundredths: 10 hundredths regroup to 1 tenth, and 10 tenths regroup to 1 unit. Both processes follow the same principle of adding like place values and regrouping based on the base-10 system.

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Solve this difference 25 9/10 – 6 4/10 7/100 by converting to hundredths.
See SolutionConvert to hundredths:
25 9/10 = 25 90/100 = 2500/100 + 90/100 = 2590/100.
6 4/10 7/100 = 6 + 40/100 + 7/100 = 6 47/100 = 600/100 + 47/100 = 647/100.
Subtract:
2590/100 – 647/100 = (2590 – 647)/100 = 1943/100.
Convert back:
1943/100 = 1900/100 + 43/100 = 19 + 43/100 = 19 43/100.

What is the difference 15 3/10 4/100 – 2 6/10 8/100? (Method shown uses vertical subtraction with multiple borrows).
See SolutionWe need to calculate 15 34/100 – 2 68/100.
Method shown in text (Regrouping steps):
15 3/10 4/100 -> 15 2/10 14/100 -> 14 12/10 14/100
– 2 6/10 8/100
—————–
12 6/10 6/100 (Subtracting place values: 14-2=12; 12/10-6/10=6/10; 14/100-8/100=6/100)
The difference is 12 66/100.

Observe the subtraction done below for 653 – 268. Do you see any similarities with the methods shown above?
Calculation shown: (Conceptual breakdown of borrowing)
(600 + 50 + 3)-(200 + 60 + 8)
= (600 – 200) + (50 – 60) + (3 – 8)
= (600 – 200) + (40 – 60) + (13 – 8) (Borrow 1 ten for ones place)
= (600 – 200) + (40 – 60) + 5
= (500 – 200) + (140 – 60) + 5 (Borrow 1 hundred for tens place)
= 300 + 80 + 5 = 385.
See SolutionYes, the similarity lies in the borrowing (or regrouping) process. When subtracting in a place value where the top digit/amount is smaller than the bottom digit/amount (like 3-8 or 50)

Figure it Out

Find the sums and differences:
(a) 3/10 + 3 4/100
See Solution0.30 + 3.04 = 3.34 (or 3 34/100)
(b) 9 5/10 7/100 + 2 1/10 3/100
See Solution9.57 + 2.13 = 11.70 (or 11 70/100 or 11 7/10)
(c) 15 6/10 4/100 + 14 3/10 6/100
See Solution15.64 + 14.36 = 30.00 (or 30)
(d) 7 7/100 – 4 4/100
See Solution7.07 – 4.04 = 3.03 (or 3 3/100)
(e) 8 6/100 – 5 3/100
See Solution8.06 – 5.03 = 3.03 (or 3 3/100)
(f) 12 6/10 2/100 – 9 9/10 9/100 (Assuming typo corrected to 12 62/100 – 9 99/100)
See Solution12.62 – 9.99 = 2.63 (or 2 63/100)

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Section 3.4 Decimal Place Value

Can we not split a unit into 4 equal parts, 5 equal parts, 8 equal parts or any other number of equal parts instead?
See SolutionYes, we absolutely can. The text shows an example where a unit is split into 4 equal parts (quarters). A length measured on this scale might be 2 2/4 units.

Then why split a unit into 10 parts every time (tenths, hundredths, etc.)?
See SolutionThe reason is consistency with our base-10 number system (the Indian or decimal place value system). In this system:
– Each place value is 10 times bigger than the place value immediately to its right (e.g., Hundreds = 10 * Tens).
– Equivalently, each place value is 10 times smaller (or 1/10) than the place value immediately to its left (e.g., Tens = Hundreds / 10).
Using tenths, hundredths, thousandths etc., for parts smaller than one unit extends this base-10 pattern logically to the right of the units place.

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Can we extend this further?
See SolutionYes, the place value system can be extended further to the right. Dividing the hundredths place (1/100) by 10 gives the thousandths place (1/1000), dividing that by 10 gives the ten-thousandths place (1/10000), and so on indefinitely.

What will the fraction be when 1/100 is split into 10 equal parts?
See SolutionSplitting 1/100 into 10 equal parts means finding 1/10 of 1/100.
Calculation: 1/10 * 1/100 = 1/1000.
The fraction will be 1/1000 (one-thousandth).

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How Big?

Introductory comparison: 100 tens = 1000; 100 hundreds = 10000.
We can ask similar questions about fractional parts:
(a): How many thousandths make one unit?
(b): How many thousandths make one tenth?
(c): How many thousandths make one hundredth?
(d): How many tenths make one ten?
(e): How many hundredths make one ten?
See Solution(a) 1 unit = 10 tenths = 100 hundredths = 1000 thousandths. So, 1000 thousandths make one unit.
(b) 1 tenth = 10 hundredths = 10 x 10 thousandths = 100 thousandths. So, 100 thousandths make one tenth.
(c) 1 hundredth = 10 thousandths. So, 10 thousandths make one hundredth.
(d) 1 ten = 10 units = 10 x 10 tenths = 100 tenths. So, 100 tenths make one ten.
(e) 1 ten = 10 units = 10 x 100 hundredths = 1000 hundredths. So, 1000 hundredths make one ten.

Make a few more questions of this kind and answer them.
See SolutionExample Question 1: How many hundredths make one hundred?
Answer: 1 hundred = 100 units = 100 x 100 hundredths = 10,000 hundredths.
Example Question 2: How many tenths make one thousand?
Answer: 1 thousand = 1000 units = 1000 x 10 tenths = 10,000 tenths.

Page 63

Make a place value table similar to the one above. Write each quantity in decimal form and in terms of place value and read the number:

(a) 2 ones, 3 tenths and 5 hundredths
See SolutionDecimal: 2.35. Place Value: 2 x 1 + 3 x 1/10 + 5 x 1/100. Read: “Two point three five”.

(b) 1 ten and 5 tenths
See SolutionDecimal: 10.5. Place Value: 1 x 10 + 0 x 1 + 5 x 1/10. Read: “Ten point five”.

(c) 4 ones and 6 hundredths
See SolutionDecimal: 4.06. Place Value: 4 x 1 + 0 x 1/10 + 6 x 1/100. Read: “Four point zero six”.

(d) 1 hundred, 1 one and 1 hundredth
See SolutionDecimal: 101.01. Place Value: 1 x 100 + 0 x 10 + 1 x 1 + 0 x 1/10 + 1 x 1/100. Read: “One hundred one point zero one”.

(e) 8/100 and 9/10 (Assuming these are parts of one number)
See SolutionDecimal: 0.98. Place Value: 0 x 1 + 9 x 1/10 + 8 x 1/100. Read: “Zero point nine eight”.

(f) 5/100
See SolutionDecimal: 0.05. Place Value: 0 x 1 + 0 x 1/10 + 5 x 1/100. Read: “Zero point zero five”.

(g) 1/10
See SolutionDecimal: 0.1. Place Value: 0 x 1 + 1 x 1/10. Read: “Zero point one”.

(h) 2 1/100 and 4 1/10 and 7 7/1000 (Assuming sum)
See SolutionDecimal: 13.117. Place Value: 1 x 10 + 3 x 1 + 1 x 1/10 + 1 x 1/100 + 7 x 1/1000. Read: “Thirteen point one one seven”.

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How can we write 234 tenths in decimal form?
See SolutionThe text explains:
234 tenths = 234/10
= 200/10 + 30/10 + 4/10
= 20 + 3 + 4/10
= 23.4

Write these quantities in decimal form: (a) 234 hundredths, (b) 105 tenths.
See Solution(a) 234 hundredths = 234/100 = 200/100 + 30/100 + 4/100 = 2 + 3/10 + 4/100 = 2.34.
(b) 105 tenths = 105/10 = 100/10 + 5/10 = 10 + 5/10 = 10.5.

Section 3.5 Units of Measurement

Length Conversion: Recall 1 cm = 10 mm (millimeters).
How many cm is 1 mm?
See SolutionSince 10 mm = 1 cm, then 1 mm = 1/10 cm = 0.1 cm.

How many cm is (a) 5 mm? (b) 12 mm?
See Solution(a) 5 mm = 5 x 1/10 cm = 5/10 cm = 0.5 cm.
(b) 12 mm = 10 mm + 2 mm = 1 cm + 2 x 1/10 cm = 1 cm + 2/10 cm = 1.2 cm.

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How many m is (a) 10 cm? (b) 15 cm?
See Solution(a) Since 1 cm = 1/100 m:
10 cm = 10 x 1/100 m = 10/100 m = 1/10 m = 0.1 m.
(b) 15 cm = 15 x 1/100 m = 15/100 m.
This can be written as 10/100 m + 5/100 m
= 1/10 m + 5/100 m = 0.1 m + 0.05 m
= 0.15 m.

Fill in the blanks below (cm <-> m conversions):
– 36 cm = 0.36 m (Since 36/100 = 0.36)
– 50 cm = 0.50 m (or 0.5 m) (Since 50/100 = 0.50)
– 89 cm = 0.89 m (Since 0.89 x 100 = 89)
– 4 cm = 0.04 m (Since 4/100 = 0.04)
– 325 cm = 3.25 m (Since 325/100 = 3.25)
– 207 cm = 2.07 m (Since 2.07 x 100 = 207)

How many mm does 1 meter have?
See Solution1 m = 100 cm. Since 1 cm = 10 mm, then 1 m = 100 x 10 mm = 1000 mm.

Can we write 1 mm = 1/1000 m?
See SolutionYes. Since 1000 mm = 1 m, dividing both sides by 1000 gives 1 mm = 1/1000 m.

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Weight Conversion

How many kilograms is 5 g?
See Solution5 g = 5 x 1/1000 kg = 5/1000 kg = 0.005 kg.

How many kilograms is 10 g?
See Solution10 g = 10 x 1/1000 kg = 10/1000 kg = 1/100 kg = 0.01 kg (or 0.010 kg).

(Calculation for 75 paise = 0.75 rupee continued from previous page):
= (70/100 + 5/100) rupee
= (7/10 + 5/100) rupee
= 0.75 rupee.

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Fill in the blanks below (rupee <-> paise conversions):
– 10 p = Rs 0.10 (Since 10/100 = 0.10)
– 5 p = Rs 0.05 (Since 0.05 * 100 = 5)
– 36 p = Rs 0.36 (Since 0.36 * 100 = 36)
– 50 p = Rs 0.50 (Since 0.50 * 100 = 50)
– 9 p = Rs 0.09 (Since 9/100 = 0.09)
– 250 p = Rs 2.50 (Since 250/100 = 2.50)

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Name all the divisions between 1 and 1.1 on the number line.
See Solution(Assuming the space between 1 and 1.1 is further divided into 10 equal parts representing hundredths, as suggested by the magnified view below it showing 1.04).
The divisions would be: 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09.

Identify and write the decimal numbers against the letters (A, B, C) on the number line shown (between 5 and 5.4).
See Solution(Note: This requires interpreting the points A, B, C on the number line image accurately).
The scale shows major markings for 5.1, 5.2, 5.3, 5.4. The space between these is divided into 10 smaller parts (hundredths).
– Point A appears to be 3 small parts past 5.1. So, A represents 5.13.
– Point B appears to be 8 small parts past 5.2. So, B represents 5.28.
– Point C appears to be 5 small parts past 5.3. So, C represents 5.35.

There is Zero Dilemma!

Sonu says that 0.2 can also be written as 0.20, 0.200; Zara thinks that putting zeros on the right side may alter the value of the decimal number. What do you think?
See SolutionSonu is correct. Adding zeros to the right of the last non-zero digit *after* the decimal point does not change the value of the number.
– 0.2 means 2 tenths (2/10).
– 0.20 means 2 tenths and 0 hundredths (2/10 + 0/100), which is still 2/10.
– 0.200 means 2 tenths, 0 hundredths, and 0 thousandths (2/10 + 0/100 + 0/1000), which is also still 2/10.
However, adding zeros between the decimal point and the non-zero digits (like 0.02 or 0.002) does change the value.
Place Value Table Explanation: It includes a table showing that 0.2, 0.20, and 0.200 all represent 2 in the tenths place and zeros elsewhere (value = 2/10). It contrasts this with 0.02 (2 in hundredths place, value 2/100) and 0.002 (2 in thousandths place, value 2/1000).

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 Can you tell which of these (0.2, 0.02, 0.002) is the smallest and which is the largest?
See Solution– 0.2 represents 2 tenths (2/10).
– 0.02 represents 2 hundredths (2/100).
– 0.002 represents 2 thousandths (2/1000).
Comparing the values: 2/1000 < 2/100 < 2/10.
Smallest: 0.002. Largest: 0.2.

Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
See SolutionWe compare them by making sure they have the same number of decimal places (adding trailing zeros doesn’t change value):
– 4.5 = 4.500
– 4.05 = 4.050
– 0.405 = 0.405
– 4.050 = 4.050
– 4.50 = 4.500
– 4.005 = 4.005
– 04.50 = 4.500 (Leading zero before decimal doesn’t change value)
Numbers with the same value are:
– Group 1: 4.5, 4.50, 04.50 (all equal 4.500)
– Group 2: 4.05, 4.050 (all equal 4.050)

Make such number lines (like Figure a) for the decimal numbers: (a) 9.876 (b) 0.407.
See Solution(This requires drawing, but the process can be described):
(a) For 9.876:
– Start with a number line showing integers (e.g., 9 and 10).
– Magnify the segment between 9 and 10, dividing it into tenths (9.1, 9.2, …, 9.9). Mark 9.8.
– Magnify the segment between 9.8 and 9.9, dividing it into hundredths (9.81, 9.82, …, 9.89). Mark 9.87.
– Magnify the segment between 9.87 and 9.88, dividing it into thousandths (9.871, …, 9.879). Mark the 6th point, which is 9.876.
(b) For 0.407:
– Start with a number line showing integers (e.g., 0 and 1).
– Magnify the segment between 0 and 1, dividing it into tenths (0.1, 0.2, …, 0.9). Mark 0.4.
– Magnify the segment between 0.4 and 0.5, dividing it into hundredths (0.41, 0.42, …, 0.49). Mark 0.40 (which is the same as 0.4).
– Magnify the segment between 0.40 and 0.41, dividing it into thousandths (0.401, …, 0.409). Mark the 7th point, which is 0.407.

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Using similar reasoning find out the decimal numbers in the boxes below (labelled d, e, f, g, h on number lines).
See Solution(Note: This requires interpreting the points on the number line images accurately).
– Number line 1 (between 4.3 and 4.8): The range is 4.8 – 4.3 = 0.5 units. This range is divided into 10 parts. So, each part represents 0.5 / 10 = 0.05 units.
– Box ‘d’ appears at the 2nd mark after 4.3. Value = 4.3 + (2 x 0.05) = 4.3 + 0.10 = 4.40.
– Box ‘e’ appears at the 7th mark after 4.3. Value = 4.3 + (7 x 0.05) = 4.3 + 0.35 = 4.65.
– Number line 2 (between 8 and 8.1): The range is 8.1 – 8 = 0.1 units. This range is divided into 10 parts. So, each part represents 0.1 / 10 = 0.01 units.
– Box ‘f’ appears at the 1st mark after 8. Value = 8 + (1 x 0.01) = 8.01.
– Box ‘g’ appears at the 4th mark after 8. Value = 8 + (4 x 0.01) = 8.04.
– Box ‘h’ appears at the 9th mark after 8. Value = 8 + (9 x 0.01) = 8.09.

Which is larger: 6.456 or 6.465?
See SolutionThe text explains the comparison method by looking at place values from left to right:
– Units place: Both numbers have 6. (Same)
– Tenths place: Both numbers have 4. (Same)
– Hundredths place: The first number has 5, the second has 6. Since 6 is greater than 5, we stop here.
Conclusion: 6.465 is larger than 6.456.

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Why can we stop comparing at this point? Can we be sure that whatever digits are there after this will not affect our conclusion?
See SolutionYes, we can stop comparing as soon as we find a place value where the digits differ. Because of the place value system (where each place is 10 times smaller than the one to its left), a difference in a higher place value (like tenths) is always more significant than any possible difference in lower place values (like hundredths, thousandths, etc.). For example, 0.41 will always be greater than 0.3999, because the difference in the tenths place (4 vs 3) outweighs any digits that follow.

Which decimal number is greater?
(a) 1.23 or 1.32
See SolutionCompare units (1 vs 1, same). Compare tenths (2 vs 3). Since 3 > 2, 1.32 is greater.
(b) 3.81 or 13.800
See SolutionCompare the whole number parts (3 vs 13). Since 13 > 3, 13.800 is greater.
(c) 1.009 or 1.090
See SolutionCompare units (1 vs 1, same). Compare tenths (0 vs 0, same). Compare hundredths (0 vs 9). Since 9 > 0, 1.090 is greater.

Closest Decimals

Consider 0.9, 1.1, 1.01, 1.11. Identify the decimal number closest to 1.
See SolutionOrder: 0.9 < 1 < 1.01 < 1.1 < 1.11.
Distances from 1:
– |1 – 0.9| = 0.1
– |1 – 1.01| = 0.01
– |1 – 1.1| = 0.1
– |1 – 1.11| = 0.11
The smallest distance is 0.01.
Therefore, 1.01 is closest to 1.

Which of the above (0.9, 1.1, 1.01, 1.11) is closest to 1.09?
See SolutionDistances from 1.09:
– |1.09 – 0.9| = 0.19
– |1.09 – 1.1| = |-0.01| = 0.01
– |1.09 – 1.01| = 0.08
– |1.09 – 1.11| = |-0.02| = 0.02
The smallest distance is 0.01.
Therefore, 1.1 is closest to 1.09.

Which among these is closest to 4: 3.56, 3.65, 3.099?
See SolutionDistances from 4:
– |4 – 3.56| = 0.44
– |4 – 3.65| = 0.35
– |4 – 3.099| = 0.901
The smallest distance is 0.35.
Therefore, 3.65 is closest to 4.

Which among these is closest to 1: 0.8, 0.69, 1.08?
See SolutionDistances from 1:
– |1 – 0.8| = 0.20
– |1 – 0.69| = 0.31
– |1 – 1.08| = |-0.08| = 0.08
The smallest distance is 0.08.
Therefore, 1.08 is closest to 1.

In each case below use the digits 4, 1, 8, 2, and 5 exactly once and try to make a decimal number as close as possible to 25.
See SolutionWe want the number to be very close to 25. We should use ‘2’ and ‘5’ for the whole number part, making it ’25’.
Then, use the remaining digits (1, 4, 8) to make the smallest possible fractional part by arranging them in ascending order after the decimal point.
Number: 25.148.
Alternatively, consider a number just below 25. Use ‘2’ and ‘4’ for the whole number part (’24’). Arrange the remaining digits (1, 5, 8) to make the largest possible fractional part (closest to 1).
Number: 24.851.
Compare distances from 25:
– |25.148 – 25| = 0.148
– |25 – 24.851| = 0.149
The smallest distance is 0.148. The number closest to 25 is 25.148.

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Addition and Subtraction of Decimals

Priya requires 2.7 m of cloth for her skirt, and Shylaja requires 3.5 m for her kurti. What is the total quantity of cloth needed? (Methods for both fractional and decimal addition are shown).
See SolutionWe need to find the sum 2.7 m + 3.5 m.
Using decimal addition (aligning decimal points):
1 (carry over)
2.7
+ 3.5
—–
6.2
The total quantity of cloth needed is 6.2 m.
(The text also shows the equivalent fractional calculation: 2 7/10 + 3 5/10 = 5 12/10 = 6 2/10, which matches 6.2).

How much longer is Shylaja’s cloth (3.5 m) compared to Priya’s (2.7 m)? (Methods for both fractional and decimal subtraction shown).
See SolutionWe need to find the difference 3.5 m – 2.7 m.
Using decimal subtraction (aligning decimal points and borrowing):
2 15 (borrow 1 unit = 10 tenths)
3.5
– 2.7
—–
0.8
Shylaja’s cloth is 0.8 m longer.
(The text also shows the equivalent fractional calculation: 3 5/10 – 2 7/10 -> 2 15/10 – 2 7/10 = 8/10, which matches 0.8).

Fill in the blanks table (g <-> kg):
– 465 g = 0.465 kg (Since 465/1000 =  0.465)
– 68 g = 0.068 kg (Since 68/1000 = 0.068)
– 1560 g = 1.560 kg (or 1.56 kg) (Since 1560/1000 = 1.560)
– 704 g = 0.704 kg (Since 704/1000 = 0.704)
– 560 g = 0.56 kg (Since 0.56 x 1000 = 560)
– 2500 g = 2.5 kg (Since 2.5  1000 = 2500)

Shows heaps/packets of rice weighing 1 g, 10 g, 100 g, 1 kg (1000 g), and 10 kg (10000 g). Each is 10 times heavier than the previous.
Fact Check: Combined weight = 10 kg + 1 kg + 100 g + 10 g + 1 g
= 10 kg + 1 kg + 0.1 kg + 0.01 kg + 0.001 kg
= 11.111 kg. (Matches text).

3. Milligram Conversion: Also, 1 gram = 1000 milligrams (mg). So, 1 mg = 1/1000 g = 0.001 g.

Rupee Paise conversion

4. Explanation: 100 paise = 1 rupee.
History of paisa coins mentioned.
1 paisa = 1/100 rupee = 0.01 rupee.

5. Example: Convert 75 paise to rupees.
See Solution75 paise = 75/100 rupee
= (70/100 + 5/100) rupee
= (7/10 + 5/100) rupee
= 0.75 rupee.

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Write the detailed place value computation for 84.691 – 77.345, and its compact form.
See SolutionCompact Form (with conceptual borrowing shown):
7 14 . 6 8 11 (Borrowed places)
8 4 . 6 9 1
– 7 7 . 3 4 5
——————
0 7 . 3 4 6

Detailed Place Value Computation:

We want to compute (80+4 + 6/10 + 9/100 + 1/1000) – (70+7 + 3/10 + 4/100 + 5/1000)
– Thousandths: 1/1000 – 5/1000. Borrow 1/100 (as 10/1000) from hundredths. Becomes 11/1000 – 5/1000 = 6/1000. Hundredths place is now 8/100.
– Hundredths: 8/100 – 4/100 = 4/100.
– Tenths: 6/10 – 3/10 = 3/10.
– Units: 4 – 7. Borrow 10 (as 10 * 1) from tens. Becomes 14 – 7 = 7. Tens place is now 70.
– Tens: 70 – 70 = 0.
Result = 0 + 7 + 3/10 + 4/100 + 6/1000 = 7.346.

Figure it Out –

Find the sums.
(a) 5.3 + 2.6 = 7.9
(b) 18 + 8.8 = 18.0 + 8.8 = 26.8
(c) 2.15 + 5.26 = 7.41
(d) 9.01 + 9.10 = 18.11
(e) 29.19 + 9.91 = 39.10 (or 39.1)
(f) 6.236 + 0.487 = 6.723
(g) 0.75 + 0.03 = 0.78

Find the differences.
(a) 5.6 – 2.3 = 3.3
(b) 18 – 8.8 = 18.0 – 8.8 = 9.2
(c) 10.4 – 4.5 = 5.9
(d) 17 – 16.198 = 17.000 – 16.198 = 0.802
(e) 17 – 0.05 = 17.00 – 0.05 = 16.95
(f) 34.505 – 18.1 = 34.505 – 18.100 = 16.405
(g) 9.9 – 9.09 = 9.90 – 9.09 = 0.81
(h) 6.236 – 0.487 = 5.749

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Similarly, identify the change and write the next 3 terms for each sequence given below. Try to do this computation mentally.
(a) 4.4, 4.45, 4.5, …
See SolutionChange: +0.05. Next 3 terms: 4.55, 4.60, 4.65.
(b) 25.75, 26.25, 26.75, …
See SolutionChange: +0.50 (or +0.5). Next 3 terms: 27.25, 27.75, 28.25.
(c) 10.56, 10.67, 10.78, …
See SolutionChange: +0.11. Next 3 terms: 10.89, 11.00, 11.11.
(d) 13.5, 16, 18.5, …
See SolutionChange: +2.5. Next 3 terms: 21.0, 23.5, 26.0.
(e) 8.5, 9.4, 10.3, …
See SolutionChange: +0.9. Next 3 terms: 11.2, 12.1, 13.0.
(f) 5, 4.95, 4.90, …
See SolutionChange: -0.05. Next 3 terms: 4.85, 4.80, 4.75.
(g) 12.45, 11.95, 11.45, …
See SolutionChange: -0.50 (or -0.5). Next 3 terms: 10.95, 10.45, 9.95.
(h) 36.5, 33, 29.5, …
See SolutionChange: -3.5. Next 3 terms: 26.0, 22.5, 19.0.

What do you think about this claim? Verify if this is true for these numbers. Will it work for any 2 decimal numbers?
See SolutionVerification for 25.936 and 8.202:
Sum = 25.936 + 8.202 = 34.138.
Check claim: Is 33 < 34.138 < 35? Yes, it is true for these numbers. Will it work for any 2 decimal numbers (let them be A.a and B.b)? – Part 1: Sum > Sum of whole parts (A+B). Sum = A.a + B.b = A + a + B + b = (A+B) + (a+b). Since a and b (the fractional parts) are always >= 0, the sum (A+B)+(a+b) will be greater than or equal to (A+B). It’s only equal if both fractional parts are zero. So, the claim should be Sum >= Sum of whole parts.
– Part 2: Sum < Sum of whole parts + 2. The fractional parts ‘a’ and ‘b’ are each less than 1 (0 <= a < 1 and 0 <= b < 1). Therefore, their sum a+b must be less than 1+1=2. So, (A+B) + (a+b) will always be less than (A+B) + 2. This part of the claim is correct.
Conclusion: The claim is essentially correct, perhaps needing slight refinement for the “greater than” part to “greater than or equal to”.

What about for the sum of 25.93603259 and 8.202?
See SolutionYes, the same logic applies regardless of the number of decimal places. The sum will be greater than or equal to 25+8=33 and less than 33 + 2 = 35.

Similarly, come up with a way to narrow down the range of whole numbers within which the difference of two decimal numbers will lie.
See SolutionLet the numbers be A.a and B.b, where A and B are whole parts, a and b are fractional parts (0 <= a < 1, 0 <= b < 1). We want to estimate A.a – B.b.
A reasonable range is: (A – B – 1) < Difference < (A – B + 1).
Example: 25.936 – 8.202 = 17.734.
Here A = 25, B = 8.
A – B-1 = 16.
A – B + 1 = 18.
The difference 17.734 lies between 16 and 18.

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Where else can we see such ‘non-decimals’ with a decimal-like notation?
See SolutionOther examples where a notation resembling decimals doesn’t follow the base-10 fractional system include:
– Time: 2.5 hours means 2 hours and 30 minutes (half an hour), not 2 hours and 50 minutes.
– Feet and Inches: Sometimes written like 2.5 ft, meaning 2 feet and 6 inches (half a foot), although 2′ 6″ is standard.
– Degrees, Minutes, Seconds (Angles/Coordinates): Although usually written with symbols (° ‘ “), sometimes might appear in pseudo-decimal forms in specific contexts.

Figure it Out

1. Convert the following fractions into decimals:
(a) 5/100
See Answer0.05
(b) 16/1000
See Answer0.016
(c) 12/10
See Answer1.2
(d) 254/1000
See Answer0.254

2. Convert the following decimals into a sum of tenths, hundredths and thousandths:
(a) 0.34
See Solution0.34 = 3 x 1/10 + 4 x 1/100
(b) 1.02
See Solution1.02 = 1 x 1 + 0 x 1/10 + 2 x 1/100
(c) 0.8
See Solution0.8 = 8 x 1/10
(d) 0.362
See Solution0.362 = 3 x 1/10 + 6 x 1/100 + 2 x 1/1000

3. What decimal number does each letter represent in the number line below? (Scale from 6.4 to 6.6 shown, divided into hundredths).
See Solution(Note: Requires interpreting the image)
– Each major mark is 0.1 (6.4, 6.5, 6.6). Each small mark is 0.01.
– ‘a’ appears 8 marks after 6.4. Value = 6.48.
– ‘b’ appears 9 marks after 6.5. Value = 6.59.
– ‘c’ appears 2 marks after 6.4. Value = 6.42.

4. Arrange the following quantities in descending order:
(a) 11.01, 1.011, 1.101, 11.10, 1.01
See Solution11.10, 11.01, 1.101, 1.011, 1.01
(b) 2.567, 2.675, 2.768, 2.499, 2.698
See Solution2.768, 2.698, 2.675, 2.567, 2.499
(c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g
See Solution4.678 g, 4.666 g, 4.656 g, 4.600 g, 4.595 g
(d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m
See Solution33.331 m, 33.313 m, 33.31 m, 33.133 m, 33.13 m

5. Using the digits 1, 4, 0, 8, and 6 make:
(a) the decimal number closest to 30
See SolutionWe need to form a number using these digits that is closest to 30. Options like 18.xxx, 40.xxx, 16.xxx etc. are possible.
– Closest below 30: 18.640? (Difference = 30 – 18.640 = 11.360)
– Closest above 30: 40.168? (Difference = 40.168 – 30 = 10.168)
The closest number seems to be 40.168.

(b) the smallest possible decimal number between 100 and 1000.
See SolutionThe number must have 3 digits before the decimal point. To be smallest, it should start with the smallest possible digit (1), followed by the next smallest (0), then the next (4). Arrange remaining digits (6, 8) after decimal.
Smallest number: 104.68.

6. Will a decimal number with more digits be greater than a decimal number with fewer digits?
See SolutionNot necessarily. Comparison depends on the place value of the digits, not the total number of digits. For example, 0.5 (one digit after decimal) is greater than 0.123 (three digits after decimal). However, if comparing whole number parts, 12 (two digits) is greater than 9 (one digit).

7. Mahi purchases 0.25 kg beans, 0.3 kg carrots, 0.5 kg potatoes, 0.2 kg capsicums and 0.05 kg ginger. Calculate the total weight.
See SolutionTotal weight = 0.25 + 0.3 + 0.5 + 0.2 + 0.05 kg.
Calculation: 0.25 + 0.30 + 0.50 + 0.20 + 0.05 = 1.30 kg.
Total weight = 1.3 kg.

8. Pinto supplies 3.79 L, 4.2 L and 4.25 L of milk in the first three days. In 6 days, he supplies 25 litres of milk. Find the total quantity supplied in the last three days.
See SolutionSupply first 3 days
= 3.79 + 4.20 + 4.25
= 12.24 L.
Total supply in 6 days = 25 L.
Supply last 3 days = Total Supply – Supply first 3 days
Supply last 3 days = 25.00 – 12.24 = 12.76 L.

9. Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
See SolutionCompare weights: 34.50 kg (Feb) < 35.75 kg (Jan). He has lost weight.
Change = Initial weight – Final weight = 35.75 – 34.50 = 1.25 kg.
He lost 1.25 kg.

10. Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, …
See SolutionThe pattern is not immediately obvious or simple (+0.9, -0.01, +0.9, -0.01, -1.1, -0.01…). It might involve alternating rules or have typos. Without a clear rule, extending it reliably is not possible.

11. How many millimeters make 1 kilometer?
See Solution1 km = 1000 m. 1 m = 1000 mm.
So, 1 km = 1000 * 1000 mm = 1,000,000 mm (One million millimeters).

12. Indian Railways insurance costs 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
See Solution1 lakh = 100,000 people.
Total fee = 100,000 people x 45 paise/person = 4,500,000 paise.
Convert to Rupees (100 paise = 1 Rupee): 4,500,000 / 100 = Rs 45,000.
The total fee is Rs 45,000.

13. Which is greater?
(a) 10/1000 or 1/10
See Solution10/1000 = 0.01. 1/10 = 0.1. Since 0.1 > 0.01, 1/10 is greater.
(b) One-hundredth or 90 thousandths?
See SolutionOne-hundredth = 1/100 = 0.01. 90 thousandths = 90/1000 = 0.090. Since 0.090 > 0.010, 90 thousandths is greater.
(c) One-thousandth or 90 hundredths?
See SolutionOne-thousandth = 1/1000 = 0.001. 90 hundredths = 90/100 = 0.90. Since 0.90 > 0.001, 90 hundredths is greater.

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14. Write the decimal forms of the quantities mentioned (an example is given):
(a) 87 ones, 5 tenths and 60 hundredths = 88.10 (Given example: 87 + 0.5 + 0.60 = 88.10)
(b) 12 tens and 12 tenths
See Solution(12 x 10) + (12 x 1/10) = 120 + 1.2 = 121.2.
(c) 10 tens, 10 ones, 10 tenths, and 10 hundredths
See Solution(10 x 10) + (10 x 1) + (10 x 1/10) + (10 x 1/100) = 100 + 10 + 1 + 0.10 = 111.10 (or 111.1).
(d) 25 tens, 25 ones, 25 tenths, and 25 hundredths
See Solution(25 x 10) + (25 x 1) + (25 x1/10) + (25 x 1/100) = 250 + 25 + 2.5 + 0.25 = 275 + 2.75 = 277.75.

15. Using each digit 0-9 not more than once, fill the boxes below so that the sum is closest to 10.5: [ . ] + [ . ]
See Solution(The format of the boxes isn’t specified, making this ambiguous. Assuming a format like [X.XX] + [Y.XX] requiring 6 unique digits total or perhaps [X.YZ] + [A.BCD] using 8 unique digits.
If we aim for exactly 10.50 using 6 digits from 0-9):
Try to get a sum of 10.50. One possibility: 6.92 + 3.58 = 10.50.
This uses digits 6, 9, 2, 3, 5, 8 (all unique).
Example Answer (assuming format allows this): 6.92 + 3.58

16. Write the following fractions in decimal form:
(a) 1/2
See Answer0.5
(b) 3/2
See Answer1.5
(c) 1/4
See Answer0.25
(d) 3/4
See Answer0.75
(e) 1/5
See Answer0.2
(f) 3/5
See Answer0.6