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## 4th grade (Eureka Math/EngageNY)

### Unit 6: Lesson 4

Topic D: Addition with tenths and hundredths- Rewriting decimals as fractions: 0.15
- Rewriting decimals as fractions: 0.8
- Rewriting decimals as fractions: 0.36
- Write decimals as fractions
- Adding fractions (denominators 10 & 100)
- Adding fractions: 7/10+13/100
- Equivalent expressions with common denominators (denominators 10 & 100)
- Add fractions (denominators 10 & 100)

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# Rewriting decimals as fractions: 0.15

CCSS.Math:

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction. Created by Sal Khan.

## Want to join the conversation?

- what if i have a number in the thousands place also?(100 votes)
- It's just the same as the tenths and hundredths..you would do the problem the same(152 votes)

- what? i have no clue what he means! pls help me(11 votes)
- Let's say you have the decimal 0.66 and you want to make it a fraction. Well, how do you say it? You say zero point six six, or sixty six hundredths, which is:

66/100 . . .

Now simplify:

33/50(23 votes)

- what if the number was bigger than the denominator(4 votes)
- You make the fraction a mixed number. For example: 24/9. 9 goes into 24 2 times right? So that's the whole number next to the fraction. 6 is left because 9 X 2=18 and 18 is 6 away from 24. Now 6 is the numerator. So now the answer is 2 6/9. Understand?(10 votes)

- How do you divide a neverending decimal?(5 votes)
- There is a way but as you say, a never ending decimal has no end so you can't get a answer that is not never ending when dividing.

e.g pi divide ? would equal 0.?(8 votes)

- I am so confused. Can someone please explain this to me?🤔(2 votes)
- Okay. If you are confused, let me tell you more.

If you have a fraction that has the numbers**10, 100,* or *1,000**in the denominator, it also has a fraction form:

.0 = tenths

.00 = hundredths

.000 = thousandths

Lets say your numerator is**19.***because

The full fraction is *19/100.*

This would be listed as *0.19

.00 = your 100th (19/**100**) so nineteen would take the place of the zeros:**0.19**

If this still doesn't make sense, say the fraction aloud:**nineteen hundredths.* That would be the same as if you said: *0.19**aloud.(9 votes)

- what if i have a number in the tenths and tens place would that be the same thing(4 votes)
- No. For example 32.5

The 3 would be in the tens place and the 5 would be in the tenths place. The tenths is used for number after the decimal point. Then, if we have 32.51, 5 would be the tenths place and 1 would be the hundredths place etc.(5 votes)

- How can you convert a repeating decimal into a percent?(1 vote)
- To convert a decimal into a percent all you have to do is multiply by 100.

Example:

0.55 * 100 = 55 Percent(4 votes)

- I have a question how to convert ( -0.38 the 8 is repeating) into a fraction ? THX(2 votes)
- Like what if the number is -0.5 with the line over the top(3 votes)
- -0.5 repeated can be written as -5/9 in fraction form.(4 votes)

- what if i have a number in the thousands place also?(3 votes)
- I'm assuming you mean thousandths place (a decimal place value).

Let's try: 0.245

Since the right most digit is in the thousandths place, the denominator = 1000

The fractions becomes: 245/1000

Then reduce the fraction. We have a common factor of 5. Divide both numerator & denominator by 5. The new fraction = 49/200

Hope this helps.(2 votes)

## Video transcript

Let's see if we can
write 0.15 as a fraction. So the important
thing here is to look at what place these
digits are in. So this 1 right over here,
this is in the tenths place, so you could view
that as 1 times 1/10. This 5 right over here is
in the hundredths place, so you could view
that as 5 times 1/100. So if I were to rewrite
this, I can rewrite this as the sum of-- this 1
represents 1 times 1/10, so that would literally
be 1/10 plus-- and this 5 represents
5 times 1/100, so it would be plus 5/100. And if we want to
add them up, we want to find a
common denominator. The common denominator is 100. Both 10 and-- the
least common multiple. 100 is a multiple
of both 10 and 100. So we can rewrite this
as something over 100 plus something over 100. This isn't going to change. This was already 5/100. If we multiply the
denominator here by 10-- that's what we did;
we multiplied it by 10-- then we're going to have to
multiply this numerator by 10. And so this is the
same thing as 10/100. And now we're ready to add. This is the same thing
as-- 10 plus 5 is 15/100. And you could have done that
a little bit quicker just by inspecting this. You would say, look, my
smallest place right over here is in the hundredths place. Instead of calling this
1/10, I could call this literally 10/100. Or I could say this
whole thing is 15/100. And now if I want to reduce
this to lowest terms, we can-- let's see, both the
numerator and the denominator are divisible by 5. So let's divide them both by 5. And so the numerator,
15 divided by 5, is 3. The denominator, 100
divided by 5, is 20. And that's about as
simplified as we can get.