Question

Write each of the following numbers in usual form:
(i) 2.06 × 10⁻⁵
(ii) 5 × 10⁻⁷
(iii) 6.82 × 10⁻⁶
(iv) 5.673 × 10⁻⁴
(v) 1.8 × 10⁻²
(vi) 4.129 × 10⁻³

Answer 1

(i) $2.06\times {10}^{-5}=\frac{206}{100}\times \frac{1}{{10}^5}=\frac{206}{{10}^2\times {10}^5}=\frac{206}{{10}^{\left(5+2\right)}}=\frac{206}{{10}^7}=\frac{206}{10000000}=0.0000206$

(ii) $5\times {10}^{-7}=\frac{5}{{10}^7}=\frac{5}{10000000}=0.0000005$

(iii) $6.82\times {10}^{-6}=\frac{682}{100}\times \frac{1}{{10}^6}=\frac{682}{{10}^2\times {10}^6}=\frac{682}{{10}^{\left(2+6\right)}}=\frac{682}{{10}^8}=\frac{682}{100000000}=0.00000682$

(iv)$5.673\times {10}^{-4}=\frac{5673}{1000}\times \frac{1}{{10}^4}=\frac{5673}{{10}^3\times {10}^4}=\frac{5673}{{10}^{\left(3+4\right)}}=\frac{5673}{{10}^7}=\frac{5673}{10000000}=0.0005673$

(v)$1.8\times {10}^{-2}=\frac{18}{10}\times \frac{1}{{10}^2}=\frac{18}{10\times {10}^2}=\frac{18}{{10}^{\left(1+2\right)}}=\frac{18}{{10}^3}=\frac{18}{1000}=0.018$

(vi) $4.129\times {10}^{-3}=\frac{4129}{1000}\times \frac{1}{{10}^3}=\frac{4129}{{10}^3\times {10}^3}=\frac{4129}{{10}^{\left(3+3\right)}}=\frac{4129}{{10}^6}=\frac{4129}{1000000}=0.004129$