Recurrent Decimals To Fraction Converter Calculator

[ 22 Votes ]

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

Recurrent Decimals To Fraction Converter Calculator
Recurrent Decimals To Fraction Converter Calculator Results (detailed calculations and formula below)
Recurrent Decimals To Fraction Converter Calculator Input Values
Recurrent Decimal (a) =

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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[ 22 Votes ]
Recurrent Decimals To Fraction Converter. This image shows the properties and recurrent decimals to fraction converter formula for the Recurrent Decimals To Fraction Converter

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,

13.729 = 13 729/1000

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

24.1 = N
241.1 = 10N
241.1 - 24.1 = 10N - N
217 = 9N
N = 217/9

Solution b

We have

8.23 = N
823.23 = 100N
823.23 - 8.23 = 100N - N
815 = 99N
N = 815/99

Solution c

We have

1.571 = N
15.71 = 10N
1571.71 = 1000N
1571.71 - 15.71 = 1000N - 10N
1556 = 990N
N = 1556/990 = 778/495

Solution d

We have

12.9 = N
129.9 = 10N
129.9 - 12.9 = 10N - N
117 = 9N
N = 117/9 = 13

Fractions Math Tutorials associated with the Recurrent Decimals To Fraction Converter Calculator

The following Math tutorials are provided within the Fractions section of our Free Math Tutorials. Each Fractions tutorial includes detailed Fractions formula and example of how to calculate and resolve specific Fractions questions and problems. At the end of each Fractions tutorial you will find Fractions revision questions with a hidden answer that reveal when clicked. This allows you to learn about Fractions and test your knowledge of Math by answering the revision questions on Fractions.