# Ex.1.3 Q6 Number System Solution - NCERT Maths Class 9

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## Question

Look at the several examples of rational numbers in the form \begin{align}\frac{p}{q}\end{align} \begin{align}(q \ne 0)\end{align} where $$p$$ and $$q$$ are integers with no common factors other than $$1$$ and having terminating decimal representation (expansions). Can you guess what property $$q$$ must satisfy?

Video Solution
Number Systems
Ex 1.3 | Question 6

## Text Solution

Steps:

We shall look at some examples of rational numbers in the form of \begin{align}\frac{{\rm{p}}}{{\rm{q}}}\end{align} \begin{align}(q \ne 0)\end{align} where decimal representations are terminating.

\begin{align}\frac{2}{5} &= 0.4 \qquad \qquad\frac{3}{{100}} = 0.03\\\\\frac{{27}}{{16}} & = 1.6875 \qquad \quad \frac{{33}}{{50}} = 0.66\end{align}

We observed that the denominators of above rational numbers are in the form of \begin{align}{2^a} \times {5^b}\end{align} Where, $$a$$ and $$b$$ are whole numbers.

Hence if $$q$$ is in the form \begin{align}{2^a} \times {5^b}\end{align} then \begin{align}\frac{{\rm{p}}}{{\rm{q}}}\end{align} is a terminating decimal.

Video Solution
Number Systems
Ex 1.3 | Question 6

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