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Class 8 RD Sharma Solutions – Chapter 2 Powers – Exercise 2.3
• Last Updated : 10 Nov, 2020

### Question 1. Express the following numbers in standard form

(i) 6020000000000000

Solution:

To express 6020000000000000 in standard form, first write it simply in the form of exponent

= 602 × 1013

There should be 1 digit before the decimal.

= 6.02 × 1015

The standard form is 6.02 × 1015

(ii) 0.00000000000942

Solution:

To express 0.00000000000942 in standard form, first write it simply in the form of exponent

= 942 × 10-14

There should be 1 digit before decimal.

The standard form is 9.42 × 10-12

(iii) 0.00000000085

Solution:

To express 0.00000000085 in standard form, first write it simply in the form of exponent

= 85 × 10-11

There should be 1 digit before decimal.

The standard form is 8.5 × 10-10

(iv) 846 × 107

Solution:

The standard form of decimal has to be expressed using 1 digit before the decimal.

= 8.46 × 102 × 107

= 8.46 × 102+7

= 8.46 × 109

The standard form is 8.46 × 109

(v) 3759 × 10-4

Solution:

The standard form of decimal has to be expressed using 1 digit before the decimal.

= 3.759 × 103 × 10-4

= 3.759 × 103 + (-4)

= 3.759 × 10-1

The standard form is 3.759 × 10-1

(vi) 0.00072984

Solution:

To express 0.00072984 in standard form, first write it simply in the form of exponent

= 72984 × 10-8

There should be 1 digit before decimal.

The standard form is 7.2984 × 10-4

(vii) 0.000437 × 104

Solution:

To express 0.000437 × 104 in standard form, first write it simply in the form of exponent

= 437 × 10-6 × 104

= 437 × 10-2

= 4.37

The standard form is 4.37

(viii) 4 ÷ 100000

Solution:

= 4/100000

The standard form is 4 × 10-5

### Question 2. Write the following numbers in the usual form:

(i) 4.83 × 107

Solution:

Usual form is written after simple multiplication

4.83 × 10000000 = 48300000

The usual form is 48300000

(ii) 3.02 × 10-6

Solution:

Usual form is written after simple multiplication

= 302 × 10-2 × 10-6

= 302 × 10-8

The usual form is 0.00000302

(iii) 4.5 × 104

Solution:

Usual form is written after simple multiplication

4.5 × 10000 = 45000

The usual form is 45000

(iv) 3 × 10-8

Solution:

The power is -8, so the decimal should shift 8 places towards the left.

The usual form is 0.00000003

(v) 1.0001 × 109

Solution:

Usual form is written after simple multiplication

1.0001 × 1000000000 = 1000100000

The usual form is 1000100000

(vi) 5.8 × 102

Solution:

Usual form is written after simple multiplication

5.8 × 100 = 580

The usual form is 580

(vii) 3.61492 × 106

Solution:

Usual form is written after simple multiplication

3.61492 × 1000000 = 3614920

The usual form is 3614920

(vii) 3.25 × 10-7

Solution:

Usual form is written after simple multiplication

= 325 × 10-2 × 10-7

= 325 × 10-9

The usual form is 0.000000325

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