NCERT Solutions for Class 8 Maths Chapter 12 Exercise 12.2 (Ex. 12.2) Exponents and Powers in PDF file format free to download for academic year 2022-2023. Get here not only PDF solution but the videos explanation also. In exercise 12.2 of class 8 mathematics questions we learn that how to write a too large or too small number in scientific notation. Every question of ex. 12.2 are properly explained step by step in explanation video.
Class 8 Maths Chapter 12 Exercise 12.2 Solution
|Chapter: 12||Exponents and Powers|
|Exercise: 12.2||Hindi and English Medium Solutions|
CBSE NCERT Class 8 Maths Chapter 12 Exercise 12.2 Solution in Hindi and English Medium
Class 8 Maths Chapter 12 Exercise 12.2 Solution in Videos
Use of Exponents to Express the Numbers in the Standard Form
The speed of light is 300,000,000 m/sec. This number is quite big and it is uneasy to read, 8 pronounce and write. We can write this number as 3 x 10⁸ m/sec. Similarly, the number 0.0000009 may be written as 9⁻⁷.
Numbers in Standard Form
A number written as a x 10ᵇ (read as a times ten raised to the power of b) is said to be in standard form, if b is an integer and a is a decimal number such that 1 ≤ a < 10.
If the number is less than 1, then the decimal point is moved to the right so that there remains only one digit on the left of the decimal.
The given number is written as the product of the number so obtained and (10)-n, where it is the number of place, the decimal point has been moved to the right.
Express each of the following numbers in standard form: (i) 6872 (ii) 140000 (iii) 15360000000
We may write
(i) 6872 = 6.872 x 1000 = (6.872 x 10³)
(ii) 140000 = 14 x 10000 = (1.4 x 10 x 10⁴) = (1.4 x 10⁵)
(iii) 15360000000 = 1536 x 10000000 = (1.536 x 1000 x 10⁷)
= (1.536 x 103 x 10⁷) = (1.536 x 10¹⁰)
The diameter of the sun is (1.4 x 10⁹) m and the diameter of the earth is (1.2756 x 10⁷) m. show that the diameter of the sun is nearly 100 times the diameter of the earth.
diameter of the sun/ diameter of the earth = (1.4 x 10⁹) /(1.2756 x 10⁷)
= (14000 x 100)/12756 = 100 (nearly)
So, (diameter of the sun) = 100 x (diameter of the earth)
Why are exponents useful when working with very large or very small numbers?
Computation with very large numbers is made easier with scientific notation. When a number is written in scientific notation, the exponent tells you if the term is a large or a small number. A positive exponent indicates a large number and a negative exponent indicates a small number that is between 0 and 1.
How do you express a large number in standard form?
Write the first number 8.
Add a decimal point after it: 8.
Now count the number of digits after 8. There are 13 digits.
So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³
How do you solve exponents without a calculator?
Write a multiplication sign between each of the base numbers that you have just written. An exponent is a number being multiplied by itself a certain number of times, and this is what you are representing when you write the multiplication signs between base numbers. Multiply out your new equation.
How do you find missing exponents?
Find The Missing Exponent
Step 1: To find the missing exponent, we have to get the same base on both sides.
Step 2: Once we get the same base, exponents can be equated and we can find the value of the missing exponent.