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### Course: MAP Recommended Practice>Unit 44

Lesson 16: Converting fractions to decimals

# Fraction to decimal with rounding

Sal writes 16/21 as a rounded decimal. Created by Sal Khan.

## Want to join the conversation?

• what does he mean at
• I know this wuestion was asked 10 years ago but i understand others may be confused as well so i’ll try my best to answer this.

Sal is saying to divide 16 by 21. Now this is because the denominator is greater than the numerator so to find the decimal, we divide 16 by 21. An easy way to remeber this is because when the numerator is greator than the denominator, it will always be 0.something. That’s how we find the decimal version.

I hope this was helpful have a great day everyone!
• could you do this with negative numbers? like:

-45
-------
-9
• Yes you could, the two negative signs would cancel out to a positive sign, and 45/9 is simply five, so the answer would be five
• Is there a quicker and more efficent way of doing this instead of going through the whole process of long division ?
• you can just divide the top number by the bottom one
• Why does he decide to round to the nearest ten thousandths, is there some sort of rule to use when dividing and deciding what to round to?
• what is this?? How do you do this??
• you can divide the top number by the bottom number or you can do what he is doing. its I little confusing for me tho because I learned this all in french but I have a good understanding of this but if the bottom number is bigger then the top number then you know the answer will be less then 1 because it cant make exactly or over one so there will be a 0. before your answer.
• how does he calculate that fast?
• Years and years of practice and doing math over and over.
• How many zeros did I need to add? and why sometimes just add three zeros? sometimes add five zeros?
• You can add as many as you like, or as many as you need when you're dividing past the decimal place.
3 zeros tend to be handy, it depends on how accurate you want the result to be

So if you want an accurate result, say 45.2836709239......... You'll want a lot of zeros. But usually you don't need a result that accurate, so maybe just use three zeros, unless otherwise told to. Most of the time they just want you to round to 2 zeros. For example 45.28
• i dont understand how he got 13 at ?
• because 160-147 = 13 there is no need to write the decimal point in this case because it is inside of long division

let me now if this helps!
• What does he mean at ?
• There are plenty of events occuring in that instant, but here are some of the things that I noticed:

Firstly, Sal brang down the zero, as it was there but unused, and 60 - 47 = 13. He just added a zero. I also saw that he said "It looks like 6 would Work". When you start to become more advanced at these types of problems, you may start to be able to estimate better.

For example, if I were to give you 101 x 99, you would probably find out pretty quickly that you could just do 100 x 100 - 1. (This works for ALL COMBINATIONS with positive integers). Anyway, the main point is that he was borrowing the zero to continue the division process, and estimated six, and he was right with some quick calculations.

Hope this helped! -`Johnny Unidas`
• how do you turn fractions w/ a negative number into a decimal? is it very different than without a negative?

## Video transcript

Let's see if we can express 16/21 as a decimal. Or we could call this 16 twenty-firsts. This is also 16 divided by 21. So we can literally just divide 21 into 16. And because 21 is larger than 16, we're going to get something less than 1. So let's just literally divide 21 into 16. And we're going to have something less than 1. So let's add some decimal places here. We're going to round to the nearest thousandths in case our digits keep going on, and on, and on. And let's start dividing. 21 goes into 1 zero times. 21 goes into 16 zero times. 21 goes into 160-- well, 20 would go into 160 eight times. So let's try 7. Let's see if 7 is the right thing. So 7 times 1 is 7. 7 times 2 is 14. And then when we subtract it, we should get a remainder less than 21. If we pick the largest number here where, if I multiply it by 21, I get close to 160 without going over. And so if we subtract, we do get 13. So that worked. 13 is less than 21. And you could just subtract it. I did it in my head right there. But you could regroup. You could say this is a 10. And then this would be a 5. 10 minus 7 is 3. 5 minus 4 is 1. 1 minus 1 is 0. Now let's bring down a 0. 21 goes into 130. So let's see. Would 6 work? It looks like 6 would work. 6 times 21 is 126. So that looks like it works. So let's put a 6 there. 6 times 1 is 6. 6 times 2 is 120. There's a little bit of an art to this. All right, now let's subtract. And once again, we can regroup. This would be a 10. We've taken 10 from essentially this 30. So now this becomes a 2. 10 minus 6 is 4. 2 minus 2 is 0. 1 minus 1 is 0. Now let's bring down another 0. 21 goes into 40, well, almost two times, but not quite, so only one time. 1 times 21 is 21. And now let's subtract. This is a 10. This becomes a 3. 10 minus 1 is 9. 3 minus 2 is 1. And we're going have to get this digit. Because we want to round to the nearest thousandth. So if this is 5 or over, we're going round up. If this is less than 5, we're going to round down. So let's bring another 0 down here. And 21 goes into 190. Let's see, I think 9 will work. Let's try 9. 9 times 1 is 9. 9 times 2 is 18. When you subtract, 190 minus 189 is 1. And we could keep going on, and on, and on. But we already have enough digits to round to the nearest thousandth. This digit right over here is greater than or equal to 5. So we will round up in the thousandths place. So if we round to the nearest thousandths, we can say that this is 0.76. And then this is where we're going around up-- 762.