Question

Without performing long division, state whether 17/160 has a terminating decimal. expansion or a non-terminating repeating decimal expansion. Write the decimal expansion if it is terminating.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{x}=\frac{17}{160}=\frac{17}{2\times 2\times 2\times 2\times 2\times 5}=\frac{17}{2^5\times 5^1} \\ \mathrm{Since}\mathrm{the}\mathrm{denominator}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{rational}\mathrm{number}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\mathrm{of}{2}^{\mathrm{n}}.5^{\mathrm{m}}, \\ \mathrm{so}\mathrm{the}\mathrm{given}\mathrm{number}\mathrm{has}\mathrm{terminating}\mathrm{decimal}\mathrm{expansion}. \\ \mathrm{Now},\mathrm{x}=\frac{17}{2^5\times 5^1}=\frac{17\times 5^4}{2^5\times 5^5}=\frac{10625}{100000}=0.10625 \end{gathered}$$