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


Practise This Question

The outer wheel of a ferris wheel is made of several steel arcs. If two arcs of equal length AB and PQ are taken, and the chord forming arc AB is measured to be 60 cm. What would be the length of chord forming arc PQ?