Now we solve for ? and simplify the fraction:Įxpress 0.84 recurring as a fraction in its lowest form.įirst, write out the equation as ? = 0.8484…įind multiples of ? that result in two equations with the same recurring digits after the decimal point, in this case:Ġ.84 recurring = 28/33 Example question 2Įxpress 0.0237237 recurring as a fraction in its lowest form. We would then move on to step three, subtracting the lesser from the greater: To resolve this, we must multiply ? = 0.03666…by 100 and also by 1000 to give us two equations with matching recurring digits: If we multiply both sides by 10 we get 10? = 0.3666… Here, the recurring digits do not match our first equation, so can’t be cancelled out. However, in most cases, step two is more complex.Īs an example, let’s take 0.03666… as our recurring decimal, so ? = 0.03666…
The above is a basic example of how to convert a recurring decimal into a fraction. In this case, both 6 and 9 are divisible by 3, so we complete our conversion by stating: When converting a recurring decimal to a fraction, we need to find its lowest form. We now take 9? = 6 and divide both sides by 9 to find our fraction: This gives us 9? = 6 Step 3: Solve for ? In this case, if we multiply both sides of ? = 0.6666… by 10, we get 10? = 6.6666…Īs our recurring digits are the same in both equations, we can subtract the lesser from the greater to cancel them out: To do this, we need a second equation with the same recurring digits after the decimal point. ? = 0.6666… Step 2: Cancel out the recurring digits Use a few repeats of the recurring decimal here.įor example, if we’re asked to convert 0.6 recurring to a fraction, we would start out with: To convert a recurring decimal to a fraction, start by writing out the equation where (the fraction we are trying to find) is equal to the given number. We’ll walk through this step by step below. Questions that require you to convert a recurring decimal to a fraction often crop up in numerical reasoning tests, so understanding the process is key. Since recurring decimals are rational numbers, they can always be expressed as fractions. For example, for 0.385385 recurring, you would see dots above both the 3 and the 5.
Where there is a longer series of repeating digits, dots appear above the first and last digits of the recurring sequence. The recurring digit or digits are typically identified by a dot placed above them, so 0.3 with a dot above the 3, or 1.745 with dots above both the 4 and 5. In this article, we’ll focus on the latter, with specific reference to recurring decimals.Ī recurring decimal, also known as a repeating decimal, is a number containing an infinitely repeating digit – or series of digits – occurring after the decimal point.
A key mathematical skill is knowing how to convert fractions to decimals and decimals to fractions. Decimals and fractions are essentially two different ways of representing the same numerical value.