Question

Without actual division find after how many decimal places will rational number $\frac{43}{5^4\times 2^3}$ will terminate and also find the decimal number.

Answer 1

$\frac{43}{5^4\times 2^3}$

$=\frac{43}{5^4\times 2^3}\times \frac{2}{2}$

$=\frac{43\times 2}{5^4\times 2^4}$

$=\frac{43\times 2}{(2\times 5{)}^4}$

$=\frac{86}{(10{)}^4}$

$=\frac{86}{10000}$

$\text{number will terminate after four decimal places and the number is 0.0086.}$