Some conversions will leave you with a numerator greater than the denominator, or an improper fraction. 3) Practice simplifying improper fractions Once you’ve listed these out, you can identify the greatest common factor to calculate the fraction’s lowest form. Knowing your times tables will help you quickly list common factors of the numerator and denominator. In a numerical reasoning test, time is of the essence, and since most recurring decimal conversions will require you to simply the fraction, you need to be able to do this at speed. You now have your two equations of 10𝓍 = 2.3434… and 1000𝓍 = 234.3434… 2) Revise your times tables The second move is 3, so add 3 zeros to 1, making your second multiple 1000. In this case the first move is 1, so add a zero to 1, making your first multiple 10. Now count the moves from the first decimal point to the second, and the first to the third. If you’re struggling to spot multiples that allow you to cancel out the recurring digits, write out the number and insert additional decimal points that leave the recurring digit to the right.įor example, if you’re converting 0.23434, your recurring digits are 34, so write out 0.2.34.34. In this instance we’ve been left with an improper fraction where the numerator is greater than the denominator, so we need to simplify this to a mixed fraction:ħ.322 recurring = 7 and 29/90 Tips for converting recurring decimals to fractions 1) Count the number of times you move the decimal point Write out the equation as 𝓍 = 0.0237237…Ġ.0237237 recurring = 79/3330 Example question 3Įxpress 7.322 recurring as a fraction in its lowest form. Now we solve for 𝓍 and simplify the fraction:Įxpress 0.84 recurring as a fraction in its lowest form.įirst, write out the equation as 𝓍 = 0.8484…įind multiples of 𝓍 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 𝓍 = 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 10𝓍 = 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 𝓍 = 0.03666…
#LA RECTORIA DE LA MIANA HOW TO#
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 9𝓍 = 6 and divide both sides by 9 to find our fraction:
This gives us 9𝓍 = 6 Step 3: Solve for 𝒳 In this case, if we multiply both sides of 𝓍 = 0.6666… by 10, we get 10𝓍 = 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. 𝓍 = 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.
#LA RECTORIA DE LA MIANA SERIES#
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. 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.
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