Question

Express the mixed recurring decimals 15.7 32 bar in p by Q form

Answer 1

let x = 15.732 (recurring Decimal)
then, 1000x= 15732.732
now, 1000x-x= 15732.732-15.732
999x= 15717
x= 15717/999
thus, 15.732 in p/q form = 15717/999
hope it was helpful!

Answer 2

15.7 32 bar in p by Q form can be represented as $\frac{15575}{990}$

Given

x=15.7 32bar

To Find

We need to express the mixed recurring decimals 15.7 32 bar in p by Q form.

Solution

Since there is one digit after decimal and not under the bar, multiply by 10 on both sides.

10x = 15.7 32bar × 10

10x = 157. 32bar

     = 157 + 0.32bar

10 x = 157 + $\frac{32}{99}$

10 x = $\frac{15575}{99}$

x = $\frac{15575}{990}$

Hence it is in the form p/q

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