Question

Express the following numbers in standard form:
(i) 6020000000000000
(ii) 0.00000000000943
(iii) 0.00000000085
(iv) 846 × 10⁷
(v) 3759 × 10⁻⁴
(vi) 0.00072984
(vii) 0.000437 × 10⁴
(viii) 4 ÷ 100000

Answer 1

To express a number in the standard form, move the decimal point such that there is only one digit to the left of the decimal point.
(i) 6020000000000000 = 6.02 x 10¹⁵ (The decimal point is moved 15 places to the left.)
(ii) 0.0000000000943 = 9.43 x 10⁻¹² (The decimal point is moved 12 places to the right.)
(iii) 0.00000000085 = 8.5 x 10⁻¹⁰ (The decimal point is moved 10 places to the right.)
(iv) 846 x 10⁷ = 8.46 x 10² x 10⁷ = 8.46 x 10⁹ (The decimal point is moved two places to the left.)
(v) 3759 x 10⁻⁴ = 3.759 x 10³ x 10⁻⁴ = 3.759 x 10⁻¹ (The decimal point is moved three places to the left.)
(vi) 0.00072984 = 7.984 x 10⁻⁴ (The decimal point is moved four places to the right.)
(vii) 0.000437 x 10⁴ = 4.37 x 10⁻⁴ x 10⁴ = 4.37 x 10⁰ = 4.37 (The decimal point is moved four places to the right.)
(viii) 4/100000 = 4 x 100000⁻¹ = 4 x 10⁻⁵ (Just count the number of zeros in 1,00,000 to determine the exponent of 10.)