| Which of the following rational number has terminating decimal expansion? |
| (i) \[\frac{26}{225}\] |
| (ii) \[\frac{5}{8}\] |
| (iii) \[\frac{2}{21}\] |
| (iv) \[\frac{7}{250}\] |
A) (i) and (ii)
B) (ii) and (iii)
C) (i) and (iii)
D) (i) and (iv)
Correct Answer: D
Solution :
| Sol. [d] \[\frac{7}{250}=\frac{7}{2\times {{5}^{3}}}\times \frac{{{2}^{2}}}{{{2}^{2}}}\] |
| \[=\frac{7\times 4}{{{(2\times 5)}^{3}}}=\frac{28}{1000}=0.028\] |
| and \[\frac{5}{8}=\frac{7}{{{2}^{3}}}\times \frac{{{5}^{3}}}{{{5}^{3}}}\] |
| \[=\frac{7\times 125}{{{(2\times 5)}^{3}}}=\frac{875}{1000}=0.875\] |
| \[\therefore \,\,\,\,\,\frac{7}{250}\] and \[\frac{5}{8}\] has terminating decimal expansion. |
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