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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