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. How do I convert recurring decimals to fractions? We’ll walk through this step by step below. A key mathematical skill is knowing how to convert fractions to decimals and decimals to fractions. 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.ĭecimals and fractions are essentially two different ways of representing the same numerical value. 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 long 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. can be expressed as 1/3.How to convert recurring decimals to fractionsĪ 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. To express a repeating decimal in fraction form, use a bar above the repeating digits. For example, 1/3 can be expressed as a repeating decimal: 0.333. Simplify the fraction to 3/4.Ī repeating decimal is a decimal in which one or more digits repeat indefinitely. For example, to convert 0.75 to a fraction, place it over 100 to get 75/100. Then, simplify the fraction if necessary. To convert a decimal to a fraction, place the decimal over a power of 10 (such as 100, 1000, etc.) that will make the decimal a whole number.
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