Name: Fractions to Decimals and Decimals to Fractions
Uploaded: 2019-07-19
Duration: 6 min 54 s
Description: When you eat ½ a pizza that is the same as 0.5 of the pizza, fractions can be converted into decimals and decimals can be converted into fractions.

Question

Check whether

0 . \bar{54}

is a pure or mixed decimal number and convert it into a fraction form.

Accepted Answer

Given recurring decimal number is $0 . \bar{54} = 0.545454 . . . . . . . . .$

The recurring decimal number, in which the recurrence of digit or digits start immediately after the decimal point, is called a pure recurring decimal number.

For example, $0.333 . . . . . . ., 1.1111 . . . . . . . .$

If the recurrence starts after one or two places of decimal, it is called mixed recurring decimal number.

For example, $2.155 . . . . . . . . ., 0.13212121 . . . . . . . .$

So, $0 . \bar{54}$ is a pure recurring decimal number.

Let $x = 0 . \bar{54}$

Now, multiplying $x$ by $100$ , we get,

$100 x = (0.5454 . . . . . . .) \times 100 = 54.5454 . . . . . . . . . .$

Let us multiply $x$ by $10000$ ,

$\Rightarrow 10000 x = (0.545454 . . . . . . . . . .) \times 10000 = 5454.5454 . . . . . .$

On subtracting $100 x$ from $10000 x$ , we get,

$10000 x - 100 x = (5454.5454 . . . . . .) - (54.5454 . . . . . . . . . .) = 5400$

$\Rightarrow 9900 x = 5400$

$\Rightarrow x = \frac{5400}{9900} = \frac{54}{99} = \frac{6}{11}$

Hence, the fraction form of $0 . \bar{54}$ is $\frac{6}{11}$ .

Check whether $0 . \bar{54}$ is a pure or mixed decimal number and convert it into a fraction form.

Important Questions on Recurring Decimal Number

Learn and Prepare for any exam you want !

Check whether 0.54¯ is a pure or mixed decimal number and convert it into a fraction form.

Important Questions on Recurring Decimal Number

Learn and Prepare for any exam you want !

Check whether $0 . \bar{54}$ is a pure or mixed decimal number and convert it into a fraction form.