… or rewrite the integer part at the beginning and simply convert the decimal part to a fraction. For the fractional part, use the modulo operator over the numerator with the denominator as a divisor. There are two ways of doing so:ĭivide the numerator and the denominator, and take the integer part of the result.
You can check it with this decimal to fraction calculator if you aren't convinced yet! You can write your decimal in several different ways, and it doesn't change the outcome of transforming it into a fraction.Īdditionally, you can convert the outcomes from an improper fraction to a mixed number. Great! a a a and b b b are precisely the same. Working out fractional exponents is more straightforward with fractions than with decimals. Writing the same number in its fractional form gives us the exact value. For instance, the number 0.4444 has a repeating decimal of 4. Part 1 Converting Basic Repeating Decimals 1 Locate the repeating decimal. Although decimals may feel more natural for writing, a few problems could arise sooner or later.įor example, by using rational numbers, we are sometimes forced to round values at some point, depending on how many significant figures we need to use. To convert a number like this to a fraction you write it as an equation, multiply, subtract to remove the repeating decimal, and solve the equation. 5 Prove algebraically that the recurring decimal 0.47 can be written as (Total for question 5 is 2 marks) 43 90 6 Prove algebraically that the recurring decimal 0.23 can be written as (Total for question 6 is 2 marks) 7 30. See the steps to convert these common decimal values to fraction form.We use numbers in everyday life, both decimals and fractions. 4 Prove algebraically that the recurring decimal 0.8 can be written as (Total for question 4 is 2 marks) 8 9. The table allows you to conveniently see the corresponding fraction for a decimal number.Ĭhart showing the conversion for common numbers from decimal to fraction Decimal Value See the fraction equivalents for some common decimal values below. And that’s all there is to it.Īn alternate method to convert a decimal to a fraction is to use a conversion chart such as this one. Then, convert the number to fraction form following the steps above.Īnd finally, add the negative sign in front of the fraction to convey that this is a negative number. Start by removing the minus sign from the beginning of the number. You can convert a negative decimal to a fraction too. The first step in transforming a repeating decimal is to create an algebraic equation to represent the decimal.ġ000x – 10x = 1178. Repeating decimal numbers require a slightly different process to convert to a fraction. Toggle Converting repeating decimals to fractions subsection. These numbers can be expressed in a rounded form, such as 1.788, or with an over-bar above the repeating portion like this: 1.1 78. 7 Converting repeating decimals to fractions. But some decimals are repeating decimals, which are numbers that continue infinitely after the decimal point, such as 1.1787878. Step 5: Solve for x, expressing your answer as. Step 4: Subtract (1) from (3) to eliminate the recurring part. So far we’ve been talking about terminating decimal numbers, since the numbers have a finite number of digits after the decimal. Step 3: Multiply recurring decimal by 10n.
#Converting recurring decimals to fractions how to#
How to Convert a Repeating Decimal to a Fraction After converting to fraction form, add the negative sign back. You can also use a fraction to mixed fraction calculator for this step.įor negative numbers, remove the negative symbol from the starting decimal, then follow the steps above. For example, let’s simplify the improper fraction 5 / 4 to a mixed number.
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