Question

without using long division so that the following rational number having a terminating decimal decimal expansion 9/80 (ii) 13/64 (iii)14588/625​

Answer 1

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Question - without using long division so that the following rational number having a terminating decimal decimal expansion 9/80 (ii) 13/64 (iii)14588/625

Answer -

Before starting

If the denominator of that number is in the form of 2 to the power or 5 to the power or both the it will have a terminating decimal expansion

Let's take 1st number 1st

9/80

Then

$80 = 2 \times 2 \times 2 \times 2 \times 5$

Therefore it will be terminating decimal expansion

Now take second number

13/64

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

Therefore it will be terminating decimal expansion

Hope it helped you