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# 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 × 10^{2 }/ 10^{14}

= 9.42 × 10^{−14 }× 10^{2}

= 9.42 × 10^{−12}

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

(iii) 6020000000000000

= 6.02 × 10^{2 }× 10000000000000

= 6.02 × 10^{2} × 10^{13}

= 6.02 × 10^{15}

Decimal has moved by 15 steps towards left.

∴ The standard form of the given number is 6.2 × 10^{15}

(iv) 0.00000000837

= 837 / 100000000000

= 8.37 × 10^{2} / 10^{11}

= 8.37 × 10^{−11}×10^{2}

= 8.37 × 10^{−9}

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

(v) 31860000000

31860000000

= 3.186 × 10^{3} × 10^{7}

= 3.186 ×10^{10}

So, decimal has moved by 10 steps towards left

∴ The standard form of the given number is 3.186 × 10^{10}

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 12

**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 × 10^{15} (iv) 8.37 × 10^{−9} and (v) 3.186 × 10^{10} respectively.

**☛ Related Questions:**

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