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CBSE Class 9 Mathematics Question 13 of 27

Number Systems — Question 6

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Question

Question 6

Look at several examples of rational numbers in the form pq\dfrac{p}{q} (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Answer

Suppose, pq\dfrac{p}{q} = 25\dfrac{2}{5} = 0.4

or

910\dfrac{9}{10} = 0.9

or

32\dfrac{3}{2} = 1.5

q must contain factors of 2 or 5 or both.

For example,

In 78\dfrac{7}{8}, 8 = 2 x 2 x 2

and

in 710\dfrac{7}{10}, 10 = 2 x 5