# Fill in the blanks.

Question:

Fill in the blanks.

(i) 360000 written in standard form is .........

(ii) 0.0000123 written in standard form is .........

(iii) $\left(\frac{-2}{3}\right)^{-2}=\ldots \ldots \ldots$

(iv) 3 × 10−3 in usual form is .........

(v) 5.32 × 10−4 in usual form is .........

Solution:

(i) The standard form of 36000 is $3.6 \times 10^{5}$.

$360000=36 \times 10^{4}=3.6 \times 10 \times 10^{4}=3.6 \times 10^{(1+4)}=3.6 \times 10^{5}$

(ii) The standard form of $0.0000123$ is $1.23 \times 10^{-5}$

$0.0000123=\frac{123}{10000000}=\frac{123}{10^{7}}=\frac{1.23 \times 100}{10^{7}}=\frac{1.23 \times 10^{2}}{10^{7}}=1.23 \times 10^{(2-7)}=1.23 \times 10^{-5}$

(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) The usual form of $3 \times 10^{-3}$ is $0.003$.

$3 \times 10^{-3}=\frac{3}{10^{3}}=\frac{3}{1000}=0.003$

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

$5.32 \times 10^{-4}=\frac{5.32}{10^{4}}=\frac{5.32}{10000}=0.000532$