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### Course: Class 9>Unit 13

Lesson 2: Number systems 1.2

# 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 begins 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.
• do it in a more less complicated way
• What is the difference between repeating decimals and a decimal that terminates?
• A repeating decimal has a group of digits that repeats infinitely many times, but a terminating decimal has only a finite number of digits.
• Where did he get the zeros all from my Elementary teacher told me use the zeros you have you cant pull them out of thin air
• Doesn’t 27 go into 190 7 times not six because 27x7 = 189?