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## Class 9 math (India)

### Course: Class 9 math (India)>Unit 1

Lesson 2: Real numbers and their decimal expansions

# Converting a fraction to a repeating decimal

Learn how to rewrite 19/27 as a repeating decimal. What's a repeating decimal? THAT is a great question. This video explains. 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.
• 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
• 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.
• 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.
• why does it always have to be the smaller number in the box and the bigger number outside the box?
• You can't think in terms of the size of the numbers to figure out what goes where.
It is always numerator (number at the top of the fraction) goes inside the box and denominator (number on the bottom of the fraction) goes outside the box. There are times where the numerator will be larger than the denominator like 17/3 = 5.66666....
• 0.13333...= 13/99
0.99999...= ?
• Interesting question!

In the real number system, 0.99999... is equal to 1! Amazing!

We can see this by considering the difference 1-0.99999... . This difference is greater than or equal to 0, but less than every decimal in the infinite sequence 0.1, 0.01, 0.001, 0.0001, 0.00001,... . The only real number that meets the conditions in the previous sentence is 0, so 1-0.99999... = 0. Therefore, 0.99999... = 1 in the real number system.