  Question

Without actual division, find which of the following rationals are terminating decimals. (i) $\frac{13}{80}$ (ii) $\frac{7}{24}$ (iii) $\frac{5}{12}$ (iv) $\frac{8}{35}$ (v) $\frac{16}{125}$

Solution

(i) Denominator of $\frac{13}{80}$ is 80. And, 80 = 24$×$5 Therefore, 80 has no other factors than 2 and 5. Thus, $\frac{13}{80}$ is a terminating decimal. (ii) Denominator of $\frac{7}{24}$ is 24. And, 24 = 23$×$3 So, 24 has a prime factor 3, which is other than 2 and 5. Thus, $\frac{7}{24}$ is not a terminating decimal. (iii)  Denominator of $\frac{5}{12}$ is 12. And, 12 = 22$×$3 So, 12 has a prime factor 3, which is other than 2 and 5. Thus, $\frac{5}{12}$ is not a terminating decimal. (iv) Denominator of $\frac{8}{35}$ is 35. And, 35 = 7$×$5 So, 35 has a prime factor 7, which is other than 2 and 5. Thus, $\frac{8}{35}$ is not a terminating decimal. (v) Denominator of $\frac{16}{125}$ is 125. And, 125 = 53 Therefore, 125 has no other factors than 2 and 5. Thus, $\frac{16}{125}$ is a terminating decimal.MathematicsRS Aggarwal (2017)Standard IX

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