Question

Fill in the blanks.
(i) 360000 written in standard form is .........
(ii) 0.0000123 written in standard form is .........
(iii) ${\left(\frac{-2}{3}\right)}^{-2}=.........$
(iv) 3 × 10⁻³ in usual form is .........
(v) 5.32 × 10⁻⁴ in usual form is .........

Answer 1

(i) The standard form of 36000 is $3.6\times {10}^5$.
$360000=36\times {10}^4=3.6\times 10\times {10}^4=3.6\times {10}^{\left(1+4\right)}=3.6\times {10}^5$

(ii) The standard form of 0.0000123 is $1.23\times {10}^{-5}$.
$0.0000123=\frac{123}{10000000}=\frac{123}{{10}^7}=\frac{1.23\times 100}{{10}^7}=\frac{1.23\times {10}^2}{{10}^7}=1.23\times {10}^{\left(2-7\right)}=1.23\times {10}^{-5}$

(iii) ${\left(\frac{-2}{3}\right)}^{-2}=\frac{9}{4}$
​${\left(\frac{-2}{3}\right)}^{-2}={\left(\frac{3}{-2}\right)}^2=\frac{3^2}{-2^2}=\frac{9}{4}$

(iv)$\mathrm{The}\mathrm{usual}\mathrm{form}\mathrm{of}3\times {10}^{-3}\mathrm{is}0.003.$
$3\times {10}^{-3}=\frac{3}{{10}^3}=\frac{3}{1000}=0.003$​

(v) $\mathrm{The}\mathrm{usual}\mathrm{form}\mathrm{of}5.32\times {10}^{-4}\mathrm{is}0.000532.$
$5.32\times {10}^{-4}=\frac{5.32}{{10}^4}=\frac{5.32}{10000}=0.000532$