Question

Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form:

(iii)$\frac{17}{320}$

Answer 1

Solution:

Step 1: Showing that the given rational number is a terminating decimal:

A rational number having the factors in the denominator as a power of $2$ or $5$ or a product of powers of $2$ and $5$ is a terminating decimal.

Given rational number is $\frac{17}{320}$

In the given rational number, the denominator has a factor as a product of powers of $2$ and $5$, that is $320=2^6\times 5$. So, it is a terminating decimal.

Step 2: Expressing in decimal form:

$$\begin{gathered} \frac{17}{320}=\frac{17}{2^6\times 5} \\ \Rightarrow \frac{17}{320}=\frac{17}{2^5\times 2\times 5} \\ \Rightarrow \frac{17}{320}=\frac{17}{32\times 10} \\ \Rightarrow \frac{17}{320}=\frac{1}{32}\times 1.7 \\ \Rightarrow \frac{17}{320}=0.053125 \end{gathered}$$

Final answer: Hence, the rational number $\frac{17}{320}$ is a terminating decimal and its decimal form is $0.053125$.