Next we want to get an equation where the repeating digit is just to the right of the decimal. If it helps, you can picture all repeating decimals with the infinity bar over them, so. If the decimal was 0.58585858, you´d only want one set of “58” on the left side. In this example, with 6 as the repeating digit, you only want one 6 on the left of the decimal. Note: You only want one “set” of repeating digit(s) on the left side of the decimal. So we multiply both sides of the equation by (10 x 1) or 10. We want that six on the left side of the decimal, which means moving the decimal place over one spot. 6667, we know that 6 is the repeating digit. Multiply by whatever value of 10 you need to get the repeating digit(s) on the left side of the decimal.įor. Let x equal the repeating decimal you´re trying to convert, and identify the repeating digit(s).Ħ is the repeating digit, and the end of the decimal has been rounded up. They´re all just different ways to show that the decimal is actually a string of 6´s that goes on forever. Since you can´t keep writing or typing the decimal out forever, they are often written as a string of digits rounded off (.666666667) or with a bar above the repeating digit(s) (. Converting a Repeating Decimal to a FractionĪ repeating decimal is one that has no end. The decimal 0.55 is equal to the fraction 11/20. 11 is a prime number and can´t be divided any more, so we know this is the fraction in its simplest form. The fraction 55/100 can be reduced by dividing both the top and bottom of the fraction by 5, giving us 11/20. For example, the fraction 3/9 isn´t in its simplest form because it can still be reduced down to 1/3 by dividing both the top and bottom of the fraction by 3.
The simplest form of the fraction is when the top and bottom of the fraction are the smallest whole numbers they can be. The final step is reducing the fraction to its simplest form. Multiplying the fraction by 100/100 gives us 55/100. 55 has two digits after the decimal point, so we´ll want to multiply the entire fraction by 10 x 10, or 100. Next, you want to multiply both the top and bottom of your new fraction by 10 for every digit to the left of the decimal point. Your first step is to write out the decimal so it looks like. Step 1įor example, say you´re given the decimal. Terminating decimals are the most common decimals you´ll see and, fortunately, they are also the easiest to convert to fractions. Converting a Terminating Decimal to a FractionĪ terminating decimal is any decimal that has a finite other of digits.
#Decimal to fraction converter chart how to#
We explain how to convert both terminating decimals and repeating decimals to fractions. If the division doesn´t come out evenly, round the decimal off.Īny decimal can be converted to a fraction by following a few steps.Divide the numerator by the denominator.If the fraction is a mixed number, change it to an improper fraction.To convert fractions to decimals you just divide the top by the bottom - divide the numerator by the denominator - and if the division doesn´t come out evenly, you can stop after a certain number of decimal places and round off. The decimal forms of rational numbers either end or repeat a pattern. You can convert all fractions to decimals.
#Decimal to fraction converter chart pdf#
Use the password worksheets.site to open the PDF file. Printable Decimal to Fraction convertion chart.
Fractions to Decimal Chart PDF Common fractions of an inch with decimal and metric equivalents.
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