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Lesson 2: Converting fractions to decimals

# Rewriting decimals as fractions: 2.75

Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How would you turn a fraction who's denominator is in the ones place like, 1 over 8 into a decimal?
• If you're familiar with division using decimals, set it up similarly to that.

EXAMPLE:

1 divided by 8 (This is what 1/8 means, technically.)

8 goes into 1 no times, so we create a decimal point and go to the tenth's place.
8 goes into 10 (which is technically 1.0) one time, leaving a 2 (which is 0.2) remaining.

Add another zero after the decimal and repeat:
8 goes into 20 (which is .20) 2 times, which leaves 4 (read 0.04) as remainder.

Put an extra zero at the end one last time:
8 goes into 40 a total of five times, with no remainder, we're done!

So with all those added zeroes left of the decimal, we get 8 goes into one... 0.125 times!
(If you weren't able to get it on you own, 1/8 = 0.125) I hope this helps!

Also, if you're still having trouble, the next video in this playlist does a great job of showing this visually:

• I can't really understand him.
• It just makes sense when you read these?
• I Don't Understand The Simpliflying Process?
• Assuming that you still dont understand, the simpliflying process is quite simple. Lets say we have a fraction of 6/21. We need to find the biggest common factor between the 2 numbers, if there is one. 6 can be divided by 2, but not 21. Because everything we do the the top, we need to do the bottom, and everything we do to the bottom we do to the top. 6 can be divided by 3, and so can 21. So, we divide 6 by 3, and get 2. We divide 21 by 3 and get 7. Our simplified answer is 2/7.
• how does this rounding work exactly? I watched the video a few times and still doesn't make sense...
• Here are some examples of fractions that need to be rounded: Example 1: The fraction 5/9 won't divide evenly — it ends in a repeating decimal. Change 5/9 to a decimal by dividing 5 by 9. If you choose to round to three decimal places, look one digit beyond the third decimal place, which is 5.To round off a decimal number, you limit the number of decimal places that the number holds. If the division ends in a repeating decimal, you can stop after a certain number of decimal places and round off.
• if the problem is 3.05 will you put 0/10
• atcually, with 3.05 you round to the nearset tenth so the real answer is 1/10
• Where did he get 25 from seriously I’m sick of math but it’s for a grade😭
• He used 25 to divide the fraction because 25 is the largest common factor that both 75 and 100 share, so he used it to simplify as much as possible, as fast as possible.
• Not sure I understand the simplification process entirely..

When Sal says you find the lowest number that both are divisible by, firstly, how does he know that so quickly (and how do you work it out) and second, when he says 25, can you not go lower? Are not 100 and 75 both divisible by 5 which is lower?
• well first of all sal is an completed school and i think he went to college
and say u have this problem
8/16
u can divide both by 4 but the lowest possible number would be 2 probably if u divide 8/16 by 4 u get 2/4
u can still simplify so if u did 8/16 by 2 u get 4/8 BUT Wait u can still simplify that by 2
so basically u need a number that will simplify another number until it cant be simplified
• What is 7/10 equal to as a decimal.
• 0.7

This is because "10" has one zero, which means one decimal place, and 7 is just how many of the 0.1's you need.
• _
On my homework my teacher gave me, it has 0.3(the three is repeated) and I have to turn that into a fraction in simplest terms. How would I convert that?
• If the three repeats forever, it is 1/3. Try doing 1 divided by 3 on a calculator. You might get something like 0.3333333334.
Write 2.75 as a simplified fraction. So once you get some practice here. You're going to find it pretty straightforward to do. But we're really going to think through it and get the intuition for why this makes sense. So if we were to write this down, the 2, that literally just represents two 1's, I'll just write it down like that. Then we have the 7 in another color. We have a 7 one place to the right of the decimal. It's in the tenths place, with a T-H-S at the end. So it literally represents 7 over 10. And then finally, we have the 5 in the hundredths place, so it represents 5 over 100. Now, if I want to write this as a simplified fraction, or really as a mixed number, I have to merge these fraction parts right here. And to add two fractions, you have to have a common denominator. And to figure out the common denominator, you just have to think about the least common multiple of 10 and 100. And that's 100. 100 is divisible by both 100 and 10. So let's get this 10 to be 100. So we can do that by multiplying it by 10. So when you multiply something by 10, you add a zero at the end of it. But you can't just do that to the denominator. We also have to do that to the numerator. So we multiplied the denominator by 10. Let's also multiply the numerator by 10. 7 times 10 is 70, or 70 over 100. It's the exact same thing as 7/10. Now we can add these two. What is 70 plus 5? 70 plus 5 is 75. And our denominator is 100, so this can be rewritten as 2 and 75/100. And we saw that in the last video, you would read this as two and seventy-five hundredths. Now we aren't in a completely simplified fraction yet because 75 and 100 have common factors. And the largest number that goes into both, if you're familiar with quarters, is 25. Three quarters is $0.75, four quarters is 100 cents, or four quarters is$1.00. So you divide both of them by 25. So 75 divided by 25 is 3, and 100 divided by 25 is 4. So as a simplified mixed number, this becomes 2 and 3/4. And after you do a lot of practice here, and you just see a lot of numbers like this, it will be almost second nature for you to say, oh, 2.75 is the same thing as 2 and 75/100, is the same thing as 2 and 3/4.