NCERT Solutions for Class 7 Maths Chapter 13 Exercise 13.3 (Ex. 13.3) Exponents and Powers in PDF file format updated as per new syllabus 2022-2023. Download the solutions in videos format or PDF, everything is free to use without any login. All the solutions are done by subject experts using easy steps, so that a student of standard 7 can understand easily.

## Class 7 Maths Chapter 13 Exercise 13.3 Solution

• ### CBSE NCERT Class 7 Maths Chapter 13 Exercise 13.3 Solution in Hindi and English Medium

 Class: 7 Mathematics Chapter: 13 Exponents and Powers Exercise: 13.3 Videos and PDF Solution

### Class 7 Maths Chapter 13 Exercise 13.3 Solution in Videos

#### Decimal Number System

Decimal system, also called Hindu-Arabic number system or Arabic number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It also requires a dot (decimal point) to represent decimal fractions.
Consider expansion of 47561, as: 47561 = 4 × 10000 + 7 × 1000 + 5 × 100 + 6 × 10 + 1

###### We can express it using powers of 10 in the exponent form:

Therefore, 47561 = 4 × 104 + 7 × 103 + 5 × 102 + 6 × 101 + 1 × 100

###### Expressing Large Numbers in The Standard Form

Large numbers can be conveniently expressed using exponents.
1. Sun is located 300,000,000,000,000,000,000 m from the centre of our Milky Way Galaxy.
2. Number of stars in our Galaxy is 100,000,000,000.
3. Mass of the Earth is 5,976,000,000,000,000,000,000,000 kg.

These numbers are not convenient to write and read. To make it convenient we use powers. Observe the following:
59 = 5.9 × 10 = 5.9 × 10¹
590 = 5.9 × 100 = 5.9 × 10²
5900 = 5.9 × 1000 = 5.9 × 10³
5900 = 5.9 × 10000 = 5.9 × 10⁴ and so on.

##### Numbers in Expanded Form

Consider the number 8604372.
Thus, in expanded form, we can write it as: 8604372 = 8 x 10⁶ + 6 x 10⁵ + 0 x 10⁴ + 4 x 10³ + 3 x 10² + 7 x 10¹ + 2 x 10⁰

### How do you find standard form?

When adding or subtracting numbers written in standard form the key is first write the numbers as ordinary number. Then add or subtract them using a standard column method. To multiply or divide numbers in standard form rearrange the sum so the numbers and powers of 10 are dealt with separately.

### What is the standard form of 200000?

200,000? 200,000 = 2 x 10⁵

### Express each of the following numbers in standard form: (i) 270659 (ii) 427500000 (iii) 6830000000

Each of the given numbers can be expressed in standard form as shown below:
(i) 270659 = 2.70659 x 10⁵
(ii) 427500000 = 4.275 x 10⁸
(iii) 6830000000 = 6.83 x 10⁹      