Class 8 Maths Exponents and Powers Use of Exponents to Express Small Numbers in Standard Form

Use of Exponents to Express Small Numbers in Standard Form

Any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 multiplied by a

power of 10. Such a form of a number is called its standard form.

Ex: Let a number is 3500

We can express this number in many ways using exponent.

3500 = 35 * 100 = 35 * 102

3500 = 350 * 10 = 350 * 101

3500 = 3.5 * 1000 = 3.5 * 103

3500 = 0.35 * 10000 = 3.5 * 104

All of these are the representation of the number 3500 in exponent form. But the standard form of the

number 3500 is that number which is expressed as number between 1 and 10.

We can express very small numbers in standard form using negative exponents.

Ex: Let we want to express 0.0053 in standard form.

0.0053 = 53/10000 = (5.3 * 10)/104 = 5.3 * 10 * 10-4 = 5.3 * 10-3

Problem: Express the following numbers in standard form:

(i) 0.0000000000085                   (ii) 0.00000000000942                  (iii) 6020000000000000

(iv) 0.00000000837                      (v) 31860000000

Solution:

(i) 0.0000000000085 = 0.0000000000085 * 1012/1012 = 8.5/1012 = 8.5* 10-12

(ii) 0.00000000000942 = 0.00000000000942 * 1012/1012 = 9.42/1012 = 9.42* 10-12

(iii) 6020000000000000 = 602 * 1015

(iv) 0.00000000837 = 0.00000000837 * 109/109 = 8.37/109 = 8.37* 10-9

(v) 31860000000 = 3.186 * 1010

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