Recurrent Decimals To Fraction Converter Calculator

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The Recurrent Decimals To Fraction Converter Calculator will calculate:

1. Any recurrent decimal into fraction

Recurrent Decimals To Fraction Converter Calculator Parameters: Enter the decimal number in this format: 12.34(27) where the number in brackets (27) represents the recuring part of the decimal

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each recurrent decimals to fraction converter calculation, the Recurrent Decimals To Fraction Converter Calculator will automatically calculate the results and update the formula elements with each element of the recurrent decimals to fraction converter calculation. You can then email or print this recurrent decimals to fraction converter calculation as required for later use.

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Theoretical description

Decimals represent another form of representing non-whole numbers. A decimal number consist of two parts, left and right, which are separated by a dot known as decimal point. The left part of a decimal represents the whole part of the number while the right part of a decimal represents the non-whole part of the number. For example, 4.7 means 4 whole items and 7 out of 10 equal parts of the fifth item.

The left (whole) part of a decimal is analogue to the whole part of a mixed number; the right (non-whole) part of a decimal is analogue to the numerator of the fractional part of a mixed number that has a power of 10 as a denominator. The number of digits in the right (after) the decimal place is equal to the number of zeroes in the denominator of the corresponding mixed number. For example,

because the whole part (on the left of decimal place) is 13 and the non-whole part is 729 out of 1000 because there are three digits after the decimal place, which means the denominator of the corresponding mixed number has 3 zeroes.

A finite decimal is easy to convert into fraction or mixed number. However, when it comes to express an infinite decimal into fraction, this becomes a challenging task, as the denominator of the corresponding fraction will have an infinite number of digits. Hence, it is impossible to write it using the method described above. Only infinite decimals with a certain recurrence (i.e. when a digit or a group of digits are repeated in a periodical fashion) can be expressed as fractions. The method is a bit particular and it is explained below.

Step 1. The original number is denoted by N.

Step 2. The original number is multiplied by a suitable power of 10 to leave only the period after the decimal point (if necessary). Thus, when written in terms of N, the number becomes that specific multiple of 10 multiplied by N.

Step 3. The new number is multiplied once again by a suitable power of 10 to leave the again same period after the decimal place (the new number now is greater than the previous one). In addition, the new number is also expressed in terms of N.

Step 4. The number obtained in the step 2 is subtracted from that obtained in the step 3. This gives the numerator of fraction.

Step 5. We do the same with these two numbers but this time it is expressed in terms of N. This gives the denominator of fraction.

Step 6. Finally, we complete the necessary simplification of the fraction obtained in the previous step. The result is the fraction form of the original recurrent decimal.

Remark! The repeating part of a recurring decimal is expressed by placing a horizontal line above the digit/s that represent the period.

Recurrent Decimals to Fractions Examples

Express the following recurring decimal as fractions.

1. 24.1
2. 8.23
3. 1.571
4. 12.9

Solution a

We have

Solution b

We have

Solution c

We have

Solution d

We have