Question

express 8.325 where 25is repeating in fraction form?

Answer 1

Let x be $8.3\overline{25}$.

Since the number of repeating decimal is 2, x and it's value should be multiplied by 100.

100x= $832.5 \overline{25}$.

Subtracting x and it's value from 100x and it's value:

100x=$832.5 \overline{25}$.
- x= 8.325.
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99x=824.2
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x=824.2/99.

Since it is still not in p/q form, we multiply the numerator and the denominator by 10 to get 8242/990.

8242/990 is the p/q form of $8.3 \overline{25}$.

Answer 2

Let x = 8.3$\bar{25}$

Reduce all extra numbers except bar numbers after decimal, To reduce multiply by 10 on both sides,

⇒ 10x = 83.$\bar{25}$ ...( i )

then, Multiply by 100 on both sides as there are 2 numbers under bar,

⇒ 1000x = 8325.$\bar{25}$ ...( ii )

Subtract 10x from ( i ) in ( ii )

1000x = 8325.$\bar{25}$

-10x = 83.$\bar{25}$

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990x = 8242

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x = $\frac{8242}{990}$

x = 8.3$\bar{25} = \frac{8242}{990}$