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