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

Convert the following mixed recurring decimal numbers to fractions: $0.2 \dot{7}, 0.0 \dot{8} \dot{1}, 2.8 \dot{2}, 0.2 \dot{7} \dot{2}$ and $3.4 \dot{3} \dot{2}$

Accepted Answer

Given mixed recurring decimals are $0.2 \dot{7}, 0.0 \dot{8} \dot{1}, 2.8 \dot{2}, 0.2 \dot{7} \dot{2}$ and $3.4 \dot{3} \dot{2}$

To convert these mixed recurring decimals into fractions, the following steps are followed.

$(i)$ At first, we write the numbers without decimal and recurring signs and subtract the digit or digits on the left of the digit or digits which are recurring. This gives the numerator of the fraction.

$(ii)$ We write as many $9$ 's as there are number of digits that are recurring and as many $0$ 's to the right side of $9$ as there are decimal places before the recurring digit or digits. This forms the denominator of the fraction.

Now, $0.2 \dot{7}$ has two decimal digits, $2$ and $7$ .

So, to convert $0.2 \dot{7}$ into a fraction, subtract $2$ from $27$ and divide by $90$

$∴ 0.2 \dot{7} = \frac{27 - 2}{90} = \frac{25}{90} = \frac{5}{18}$

Similarly,

$0.0 \dot{8} \dot{1} = \frac{81 - 0}{990} = \frac{81}{990} = \frac{9}{110}$ ,

$3.4 \dot{3} \dot{2}$ ,

$0.2 \dot{7} \dot{2} = \frac{272 - 2}{990} = \frac{270}{990} = \frac{30}{110}$ and

$3.4 \dot{3} \dot{2} = \frac{3432 - 34}{990} = \frac{3398}{990}$

Hence, the given mixed recurring decimal number have been converted to fractions.

Convert the following mixed recurring decimal numbers to fractions: $0.2 \dot{7}, 0.0 \dot{8} \dot{1}, 2.8 \dot{2}, 0.2 \dot{7} \dot{2}$ and $3.4 \dot{3} \dot{2}$

Important Questions on Recurring Decimal Number

Learn and Prepare for any exam you want !

Convert the following mixed recurring decimal numbers to fractions: 0.27˙, 0.08˙1˙, 2.82˙, 0.27˙2˙ and 3.43˙2˙

Important Questions on Recurring Decimal Number

Learn and Prepare for any exam you want !

Convert the following mixed recurring decimal numbers to fractions: $0.2 \dot{7}, 0.0 \dot{8} \dot{1}, 2.8 \dot{2}, 0.2 \dot{7} \dot{2}$ and $3.4 \dot{3} \dot{2}$