# RD Sharma Solutions Class 8 Powers Exercise 2.3

## RD Sharma Solutions Class 8 Chapter 2 Exercise 2.3

### RD Sharma Class 8 Solutions Chapter 2 Ex 2.3 PDF Download

#### Exercise 2.3

1. Express the following numbers in standard form:

(i) 6020000000000000

(ii) 0.0000000000943

(iii) 0.00000000085

(iv) $846 \times 10^{7}$

(v) $3759 \times 10^{-4}$

(vi) 0.00072984

(vii) $0.000437 \times 10^{4}$

(viii) $4 \div 100000$

Answers:

To express a number in the standard for, move the decimal point such that there is only one digit to the left of the decimal point.

(i) 6020000000000000 = $6.02 \times 10^{15}$ (The decimal point is moved 15 places to the left.)

(ii) 0.0000000000943 = $9.43 \times 10^{-12}$ (The decimal point is moved 12 places to the right.)

(iii) 0.00000000085 = $8.5 \times 10^{-10}$       (The decimal point is moved 10 places to the right.)

(iv) $846 \times 10^{7} = 8.46 \times 10^{2} \times 10^{7} = 8.46 \times 10^{9}$  (The decimal point is moved two places to the left.)

(v) $3759 \times 10^{-4} = 3.759 \times 10^{3} \times 10^{-4} = 3.759\times 10^{-1}$    (The decimal point is moved three places to the left.)

(vi) $0.00072984 = 7.984 \times 10^{-4}$         (The decimal point is moved four places to the right.)

(vii) $0.000437 \times 10^{4} = 4.37 \times 10^{-4} \times 10^{4} = 4.37 \times 10^{0} = 4.37$        (The decimal point is moved four places to the right.)

(viii) $4 \div 100000 = 4 \times 100000^{-1} = 4 \times 10^{-5}$        (Just count the number of zeros in 1,00,000 to determine the exponent of 10.)

2. Write the following numbers in the usual form:

(i) $4.83 \times 10^{7}$

(ii) $3.02 \times 10^{-6}$

(iii) $4.5 \times 10^{4}$

(iv) $3 \times 10^{-8}$

(v) $1.0001 \times 10^{9}$

(vi) $5.8 \times 10^{2}$

(vii) $3.61492 \times 10^{6}$

(viii) $3.25 \times 10^{-7}$

Answers:

(i) $\; 4.83 \times 10^{7} = 4.83 \times 1,00,00,000 = 4,83,00,000$

(ii) $\; 3.02 \times 10^{-6} = \frac{3.02}{10^{6}} = \frac{3.02}{10,00,000} = 0.00000302$

(iii) $\; 4.5 \times 10^{4} = 4.5 \times 10,000 = 45,000$

(iv) $\; 3 \times 10^{-8} = \frac{3}{8} = \frac{3}{10,00,00,000} = 0.00000003$

(v) $\; 1.0001 \times 10^{9} = 1.0001 \times 1,00,00,00,000 = 1,00,01,00,000$

(vi) $\; 5.8 \times 10^{2} = 5.8 \times 100 = 580$

(vii) $\; 3.61492 x 10^{6} = 3.61492 x 10,00,000 = 3614920$

(viii) $\; 3.25 x 10^{-7} = \frac{3.25}{10^{7}} = \frac{3.25}{1,00,00,000} = 0.000000325$