hEorpaigh3tR

2022-11-26

Write down the decimal expansions of : 15/1600

Theresa Sims

Expert

We have: $\frac{15}{1600}=\frac{15}{64×25}=\frac{15}{{2}^{6}×{5}^{2}}$
$\begin{array}{cc}2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$
To get the denominator as multiple of 10's, multiply numerator and denominator by ${5}^{4}$
$=\frac{15×{5}^{4}}{{2}^{6}×{5}^{2}×{5}^{4}}$
$=\frac{15×{5}^{4}}{{2}^{6}\ast {5}^{6}}$
$=\frac{15×{5}^{4}}{{10}^{6}}$ [Since, ${a}^{m}×{b}^{m}=\left(ab{\right)}^{m}$]
$=\frac{9375}{{10}^{6}}$
$=\frac{0009375}{1000000}$
Since we have six zeroes in the denominator, we need to put the decimal point after six digits from the unit place.
Hence, the decimal expansion of the given number is 0.009375

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