Express the following numbers in standard form.
(i) 0.0000000000085    (ii) 0.00000000000942
(iii) 6020000000000000    (iv) 0.00000000837
(v) 31860000000

Solution:

Standard form of exponents is used to represent a very small or large number following a certain set of rules.

(i) 0.0000000000085

To convert this small number into the standard form we need to move the decimal to its right by 12 steps.

= 85/10000000000000

= 85/10000000000000

= 8.5 × 10/10¹³

= 8.5 × 10^-13 × 10

= 8.5 × 10^-12

∴ The standard form of a given number is 8.5 × 10^-12

(ii) 0.00000000000942

= 942/100000000000000 

= 9.42 × 10² / 10¹⁴

= 9.42 × 10⁻¹⁴ × 10²

= 9.42 × 10⁻¹²

∴ The standard form of a given number is 9.42 × 10⁻¹²

(iii) 6020000000000000

= 6.02 × 10² × 10000000000000

= 6.02 × 10² × 10¹³

= 6.02 × 10¹⁵

Decimal has moved by 15 steps towards left.

∴ The standard form of the given number is 6.2 × 10¹⁵

(iv) 0.00000000837

= 837 / 100000000000

= 8.37 × 10² / 10¹¹

= 8.37 × 10⁻¹¹×10²

= 8.37 × 10⁻⁹

∴ The standard form of a given number is 8.37 × 10⁻⁹

(v) 31860000000

31860000000

= 3.186 × 10³ × 10⁷

= 3.186 ×10¹⁰

So, decimal has moved by 10 steps towards left

∴ The standard form of the given number is 3.186 × 10¹⁰

☛ Check: NCERT Solutions for Class 8 Maths Chapter 12

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Video Solution:

Express the following numbers in standard form. (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000

Class 8 Maths NCERT Solutions Chapter 12 Exercise 12.2 Question 1

Summary:

The following numbers are expressed in their standard form (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000 as follows  (i) 8.5 × 10^-12 (ii)  9.42 × 10⁻¹² (iii)  6.02 × 10¹⁵ (iv) 8.37 × 10⁻⁹ and (v)  3.186 × 10¹⁰ respectively.

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