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### Course: 8th grade (Illustrative Mathematics)>Unit 8

Lesson 15: Lesson 14: Decimal representations of rational numbers

# Converting a fraction to a repeating decimal

To convert a fraction like 19/27 into a decimal, you should divide 27 into 19, and use the remainder to figure out the decimal. The decimal is 0.703703, and the notation for a repeating decimal like this is to write the numbers that repeat and then put a line above them. The first six digits of the decimal should be included in the answer. Created by Sal Khan.

## Want to join the conversation?

• Is there a way to convert a repeating decimal back into a fraction? I just can't work it out.
• is 8th grade math important in college?
• Unlike some other subjects, Math builds on itself, so the concepts in 8th grade will be very important to do 9th grade Algebra and 10th grade Geometry which is needed to move to Algebra II, pre-calculus and calculus in college. For most degrees, you have to take some math classes.
• how do you know how many 0s to put down?
• Supposed you've reached the stage of putting down only zeros after the decimal point from the dividend (inside number).
Continue putting down zeros either until the remainders begin to repeat, or until a remainder is 0.
In the first case, look at the repeating group of remainders. Consider the digit in the answer that is computed just after each remainder in the repeating group is found. These digits form the repeating group in the answer; the answer becomes a repeating decimal.
In the second case, there are no more decimal digits to put in the answer; the answer is a terminating decimal.

Have a blessed, wonderful day!
• I'm really confused where you got those 0's from and why it's such a big equation
• No were, hes using it to make the number bigger so he can divide it.
• GET ME TO 100 UP VOTES AND I WILL DONATE \$100 dollars to Khan Academy
• no one wants you to do that
• Why is a repeating decimal has only 6 digits?
• They have an infinite number of digits. But since it would take a while to write that many, he stops when he has written enough for the pattern to become visible.
• does it change if you get a three digit number as the denominator, or numerator
• No- you still have to divide the denominator into the numerator no matter what. You’d have a harder time doing that, though