Question

Write down the decimal expansions of : $\frac{15}{1600}$

Answer 1

Given $\frac{15}{1600}=\frac{15}{64\times 25}=\frac{15}{2^6\times 5^2}$

$\begin{array}{cc}2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$

To get the denominator as multiple of $10$'s, multiply numerator and denominator by $5^4$

$=\frac{15\times 5^4}{2^6\times 5^2\times 5^4}$

$=\frac{15\times 5^4}{2^6{.5}^6}$

$=\frac{15\times 5^4}{{10}^6}$ [Since, $a^m\times b^m=(ab{)}^m$]

$=\frac{9375}{{10}^6}$

$=\frac{0009375}{1000000}$

Since, we have $6$ zero's in the denominator, so we need to put the decimal point after 6 digits from the unit place.
Therefore, the decimal expansion of the given number is $0.009375$