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## 7th grade

### Course: 7th grade > Unit 2

Lesson 2: Converting fractions to decimals- Rewriting decimals as fractions: 2.75
- Rewriting decimals as fractions challenge
- Worked example: Converting a fraction (7/8) to a decimal
- Fraction to decimal: 11/25
- Fraction to decimal with rounding
- Converting fractions to decimals
- Comparing rational numbers
- Order rational numbers

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# 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 at0:17(78 votes)
- 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!(7 votes)

- could you do this with negative numbers? like:

-45

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-9(15 votes)- 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(19 votes)

- Is there a quicker and more efficent way of doing this instead of going through the whole process of long division ?(10 votes)
- you can just divide the top number by the bottom one(7 votes)

- 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?(13 votes)
- idk uyghbjhuil bll kjvk, vl.(0 votes)

- what is this?? How do you do this??(8 votes)
- 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.(5 votes)

- how does he calculate that fast?(6 votes)
- Years and years of practice and doing math over and over.(13 votes)

- i saw a raccoon at a tree(8 votes)
- How many zeros did I need to add? and why sometimes just add three zeros? sometimes add five zeros?(6 votes)
- 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(3 votes)

- yo this video is pi minutes long (3.14)(6 votes)
- What does he mean at1:30?(3 votes)
- 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`

(5 votes)

## 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.