Question

Express the following numbers in the standard form:
(i) 3908.78
(ii) 5,00,00,000
(iii) 3,18,65,00,000
(iv) 846 × 10⁷
(v) 723 × 10⁹

Answer 1

We have

(i) 3908.78 = 3.90878 x 10³ [since the decimal point is moved 3 places to the left]

(ii) 5,00,00,000 = 5,00,00,000.00 = 5 x 10⁷ [since the decimal point is moved 7 places to the left]

(iii) 3,18,65,00,000 = 3,18,65,00,000.00
= 3.1865 x 10⁹ [since the decimal point is moved 9 places to the left]

(iv) 846 × 10⁷ = 8.46 x 10² x 10⁷ [since the decimal point is moved 2 places to the left]
= 8.46 x 10⁹ [since a^m x aⁿ = a^m+n]

(v) 723 × 10⁹ = 7.23 x 10² x 10⁹ [since the decimal point is moved 2 places to the left]
= 7.23 x 10¹¹ [ since a^m x aⁿ = a^m+n]