Question

the following real numbers have decimal expansions as given below. In each case decide whether they are rational or not. If they are rational and of the forrm p/q write prime factors of q so that p and q are co-prime.
1) 0.131141115 2)0.675

Answer 1

$$\begin{gathered} \left(1\right)0.131141115 \\ \mathrm{Here}\mathrm{decimal}\mathrm{is}\mathrm{terminating}. \\ \mathrm{Therefore}\mathrm{it}\mathrm{is}\mathrm{rational}\mathrm{number}. \\ \mathrm{Now}, \\ 0.131141115=\frac{131141115}{1000000000}=\frac{26228223}{200000000} \\ \left(2\right)0.675 \\ \mathrm{Here}\mathrm{decimal}\mathrm{is}\mathrm{terminating}. \\ \mathrm{Therefore}\mathrm{it}\mathrm{is}\mathrm{rational}\mathrm{number}. \\ \mathrm{Now}, \\ 0.675=\frac{675}{1000}=\frac{27}{40} \end{gathered}$$