How to use the decimal to portion cpositiveeast.orgtor.

You are watching: .13 repeating as a fraction

This cpositiveeast.orgtor permits you to transform real numbers, including repeating decimals, into fractions.

Enter a decimal number in the room above, then press Convert come Fraction come send the number and also cpositiveeast.orgte the indistinguishable fraction.

Number formats

You may get in simple reasonable numbers with the whole section separated from the decimal portion by a decimal allude (ex. 12.25). You may additionally convert to fractions numbers through infinitely repeating digits by enclosing the repeating digits in parenthesis or by including "..." at the end of the number. See the adhering to table for examples:

kind of numberExampleWhat to enterResult simple decimal Repeating decimal Repeating decimal Repeating sequence
0.30.3... Or 0.(3)1/3
0.1230.1233... Or 0.12(3)37/300
0.7450.74545... Or 0.7(45)41/55

How to convert a decimal number come it"s tantamount fraction

When the number has actually no repeating decimal portion, the numerator of the identical fraction is obtained by removed the period from the number, and also the denominator is "1" followed by the same variety of 0"s as the size of the decimal portion.

For example the number 12.4 is same to 124 split by 10, so the equivalent portion is 124/10, which, as soon as simplified, becomes 62/5.

This is due to the fact that the number is multiply by a strength of 10 such the the decimal suggest is removed. The resulting number is then shown divided by the same power that 10 to stand for the initial number as a fraction.

When the number has actually infinitely repeating decimals, then the portion is acquired by breaking the number right into a sum of the non-repeating section and the repeating portion. Each aspect is convert separately, the no repeating portion is convert as described above, when the portion for the repeating part is obtained by dividing the repeating numbers by a number of 9"s same to the size of the sequence, complied with by a number of "0"s equal to the the number of 0"s between the dot and the repeating digits.

For example the number 2.5333... Is damaged into the sum 2.5+0.0333, 2.5 becomes 5/2 and also 0.0333 becomes 33/990 or,simplified, 1/30. The an outcome of the conversion is because of this (5/2)+(1/30)=38/15

All fractions are reduced as shortly as possible to leveling the subsequent operations.

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When the number can not be converted

Very huge numbers or numbers with plenty of digits after the floating point may no be convert here. When the equivalent fraction cannot it is in cpositiveeast.orgted, the error "Sorry, overflow error" will certainly be displayed.