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## 5th grade (Eureka Math/EngageNY)

### Course: 5th grade (Eureka Math/EngageNY) > Unit 4

Lesson 7: Topic G: Division of fractions and decimal fractions- Relate fraction division to fraction multiplication
- Visually dividing whole numbers by unit fractions
- Dividing whole numbers by unit fractions visually
- Dividing a whole number by a unit fraction
- Dividing whole numbers by unit fractions
- Visually dividing unit fraction by a whole number
- Dividing unit fractions by whole numbers visually
- Dividing a unit fraction by a whole number
- Dividing unit fractions by whole numbers
- Dividing whole numbers by fractions: word problem
- Dividing fractions by whole numbers: studying
- Divide fractions and whole numbers word problems
- Fraction and whole number division in contexts
- Rewriting a fraction as a decimal: 3/5
- Rewriting a fraction as a decimal: 21/60
- Fractions as division by a multiple of 10
- Dividing decimals
- Divide decimals by whole numbers
- Divide decimals like 16.8÷40 by factoring out a 10

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# Rewriting a fraction as a decimal: 21/60

Sal rewrites 21/60 as a decimal. Created by Sal Khan.

## Want to join the conversation?

- Is there a millionths place?(28 votes)
- Yes. The 1st number to the right of the decimal is the tenths place (1/10 or 0.1). The 2nd number to the right of the decimal is the hundreths place (1/100 or 0.01). The 3rd number to the right of the decimal is the thousandths place (1/1,000 or 0.001). The 4th number to the right of the decimal is the ten thousandths place (1/10,000 or 0.0001). The 5th number to the right of the decimal is the hundred thousandths place (1/100,000 or 0.00001). AND, the 6th number to the right of the decimal is the millionths place. So, .000001 is equal to 1/1,000000 which is one millionth. Hope this helps. Good Luck.(53 votes)

- How to get the greatest common multiple of two numbers if they are both too big? Then I won't be able to simplify the fraction?(7 votes)
- how would you convert hundreths to tenths(5 votes)
- 100 divided by 10 is equal to 10. Therefore, we divide the numerator and denominator( the denominator is 100) by 10 to convert hundredths to tenths (the denominator will now be 10).(7 votes)

- is there a trillionths place? or more?(4 votes)
- Yup! There's a quadrillionths place, octillionths place, and more. In fact, for any name of a large number, you can add the "-ths" for its inverse, for infinitely many numbers: https://en.wikipedia.org/wiki/Names_of_large_numbers(5 votes)

- I think not every number will result in a product that is divisible by 10. So I think in that case, you might have to do long division.(5 votes)
- You're right. For example, 50/23. Here we just directly divide 50 and 23.(3 votes)

- I don't think every number will result in a product that's divisible by 10, so in this case, you have to do long division. Also, I don't know what was the point of the 3/5 + 5/100. Don't know what Sal was trying to show.(4 votes)
- For the 30/100 + 5/100, Sal was trying to show why we call 0.35 thirty five hundredths. "We have 5 in the hundredths place but why do we call it thirty five hundredths?" Sal said three tenths (3/10) is the same as thirty hundredths (30/100). So we add 30/100 and 5/100 together to get 35 hundredths.(4 votes)

- Up to how many decimal places can there be?(4 votes)
- There are an infinite number of possible places. As we get off the the right, however, the places start to get less and less important. Usually, you will round off to 3 or 4 places.(4 votes)

- Write each as a decimal and fraction . Four and nine hundred this decimal.(4 votes)
- Four and nine hundredths is the written form, 4.09 is the decimal form, 4 9/100 is the mixed number form, and 409/100 is the improper fractional form.(2 votes)

- what if the denominator is over one hundred?(4 votes)
- when you are doing a fraction of 21/60 i dont understad were the 3 is coming from ?(3 votes)
- I can probably help you here, but what do you mean 'where is the 3 coming from?'(2 votes)

## Video transcript

Let's see if we can
write 21/60 as a decimal. And I'll give you a little hint. See if you can rewrite
this as a fraction with 100 as the denominator. Or another way to say it is
see if you can rewrite this so it's a certain
number of hundredths, and then you can represent
that as a decimal. So we've done this before. We can rewrite a fraction. We can get an
equivalent fraction if we either multiply the
numerator and the denominator by the same quantity
or we divide the numerator and
the denominator by the same quantity. And this numerator and
this denominator, it looks pretty clear. 21 is divisible by 3
and 7 and 1 and 21. And 60 is clearly
divisible by 3 as well. It's not divisible by 7 or 21. Well, of course,
it's divisible by 1, but that doesn't
really help you much. So let's see if we can
rewrite this, maybe with lower numbers,
where we divide both the numerator and
the denominator by that common factor of 3. So we're dividing by 3. So I'm just rewriting this as
an equivalent fraction that might make it a little
bit easier for our heads to get around it. So 21 divided by
3 is equal to 7. And 60 divided by
3 is equal to 20. So we've rewritten
21/60 as 7/20. So you might be saying, Sal,
why did you even do this? Aren't we trying to get
it in terms of hundredths? Well, this one helps simplify
it in my brain a little bit. And what's extra good
about writing it as 7/20 it is that it's easier
to go from 20 to 100. To go from 20 to 100 we
just have to multiply by 5. Well, if each section is going
to be five times as many then these seven sections are going
to be five times as many. So, once again, we're
multiplying the numerator and the denominator
by the same thing. And so this is going to be
equal to 35 over 100, or 35/100. 35-- let me write it
a little bit-- 35/100, which is what we wanted to do. We wanted to rewrite this
in terms of hundredths. And what is 35/100? Well, let's just
remind ourselves when we're writing a decimal,
that's the ones place. This right over here, this next
place, is the tenths place. And the next place is
the hundredths place. And so 35/100, well, you
could write that like this. You could write that
as 35 hundredths. So you could literally
write this as 0.35. And you might say, wait, you
put a 3 in the tenths place. Why is this 35 hundredths? I get that this is 5 hundredths,
but why is this 35 hundredths? Well, 3/10 is 30/100. So this is 35/100. Or another way of
thinking about it, you could rewrite
this right over here. You could rewrite this as being
equal to 30/100 plus 5/100. And what is 30 over
100 if you wanted to rewrite it in
terms of tenths? Well, you could just divide the
numerator and the denominator by 10, and you would
get 3/10 plus 5/100. And we see that right
over here, 3/10, that's the tenths place, plus
5/100, that's hundredths place. Or this is sometimes
referred to as 35/100.