![]() ![]() But in this case, none of this really matters since the value of the number is exactly the same no matter how it’s written. How? Well, since you can always attach an infinite number of zeros to the very end of a number without changing its value, you can put an infinitely long string of zeros on the end of an otherwise terminating decimal…and you’ll have turned it into a repeating decimal!įor example, you can think of the terminating decimal 0.25 as 0.25000… instead. If you think about it though, you’ll see that any terminating decimal number can actually be written as a repeating decimal too. (Remember, a decimal that just goes on and on with no repeating pattern is irrational.) Can a Terminating Decimal Be Written as a Repeating Decimal? So a repeating decimal is a rational number whose decimal representation has some repeating pattern, and a terminating decimal is a rational number whose decimal representation eventually stops. 9/11 = 0.818181… is another repeating decimal since the pattern of digits “81” repeat forever.7/9 = 0.7777… is a repeating decimal since 7 goes on forever.3/5 = 0.6 is another terminating decimal number.1/3 = 0.3333… is a repeating decimal since the number 3 goes on forever.1/4 = 0.25 is a terminating decimal since it has a finite number of decimal digits.To see what the difference is, let’s take a look at a few examples of decimal representations of rational numbers: When the equivalent fraction cannot be calculated, the error "Sorry, overflow error" will be displayed.What are Terminating and Repeating Decimals?īefore we get into the details of how to actually convert terminating and repeating decimals into opens in a new windowfractions, we’d better make sure we understand what it means for a rational number to be a “terminating” or “repeating” decimal in the first place. Very big numbers or numbers with many digits after the floating point may not be converted here. The result of the conversion is therefore (5/2)+(1/30)=38/15Īll fractions are reduced as soon as possible to simplify the subsequent operations. Each element is converted separately, the non repeating portion is converted as explained above, while the fraction for the repeating portion is obtained by dividing the repeating figures by a number of 9's equal to the length of the sequence, followed by a number of '0's equal to the the number of 0's between the dot and the repeating digits.įor example the number 2.5333. When the number has infinitely repeating decimals, then the fraction is obtained by breaking the number into a sum of the non-repeating portion and the repeating portion. The resulting number is then shown divided by the same power of 10 to represent the original number as a fraction. This is because the number is multiplied by a power of 10 such that the decimal point is removed. When the number has no repeating decimal portion, the numerator of the equivalent fraction is obtained by removing the dot from the number, and the denominator is '1' followed by the same number of 0's as the length of the decimal portion.įor example the number 12.4 is equal to 124 divided by 10, so the equivalent fraction is 124/10, which, when simplified, becomes 62/5. How to convert a decimal number to it's equivalent fraction See the following table for examples: Type of number You may also convert to fractions numbers with infinitely repeating digits by enclosing the repeating digits in parenthesis or by adding '.' at the end of the number. You may enter simple rational numbers with the whole portion separated from the decimal portion by a decimal point (ex. This calculator allows you to convert real numbers, including repeating decimals, into fractions.Įnter a decimal number in the space above, then press Convert to Fraction to send the number and calculate the equivalent fraction. How to use the decimal to fraction calculator. ![]()
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