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### Course: 4th grade (Eureka Math/EngageNY) > Unit 6

Lesson 1: Topic A: Exploration of tenths- Relating decimals and fractions in words
- Relate decimals and fractions in words
- Decimal place value
- Decimals as words
- Decimals in words
- Graphing tenths from 0 to 1
- Decimals on the number line: tenths 0-1
- Identifying tenths on a number line
- Decimals on the number line: tenths
- Equivalent fractions with fraction models (denominators 10 & 100)

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# Relating decimals and fractions in words

Sal relates equivalent decimals and fractions written in word form.

## Want to join the conversation?

- How do you multiply fractions?(12 votes)
- To multiply two fractions, you would take their numerators (the number on top of the line) and multiply them as you would any other numbers. Then, take the denominators (the numbers on the bottom of the line) and multiply them together. Your answer should be the product of the numerators above the product of the denominators.(14 votes)

- Why is there no ones place in decimals?(3 votes)
- The decimal place value tells you the denominator of the fraction that the digit represents. For example:

0.1 = 1 tenth = 1/10

0.01 = 1 hundredth = 1/100

So if you had a oneth place, what would you get? You would have 1/1 = 1 (a whole number). You're back to the ones place which is on the left side of the decimal.

Hope this helps.(16 votes)

- so can decimals go forever(5 votes)
- Are decimals like fractions with wholes to the left along with a decimal point?(4 votes)
- Yes that is right. In a decimal, the whole number part is to the left of the decimal point, and the fractional part is to the right of it.

Have a blessed, wonderful day!(9 votes)

- how long is the right of the decimal(3 votes)
- What would you need decimals for in life?(2 votes)
- Decimals are most often used with money. $1.23 That means that when you are buying something you will probably see a decimal. It is also good to know how to convert fractions to decimals as they appear cleaner and can be used easier in some cases. Instead of 1 1/2, we could simply write 1.5. I hope this helps! If you have any questions be sure to let me know.(6 votes)

- Why do fractions have to be more exact? I like decimals more. :((2 votes)
- Some fractions convert to decimals that have infinitely many digits. For those fractions, using a finite number of decimal digits gives an approximation. For example, if we want to express 2 out of 3 equal parts, the exact answer is 2/3, but something like 0.667 is an approximation. The decimal for 2/3 has infinitely many digits.(6 votes)

- what about converting decimals to fractions(2 votes)
- For decimals with a finite number of digits, ignore the decimal point to find the numerator. The denominator is based on the place value of the last digit (furthest to the right). Then reduce as needed.

Example: convert 0.048 into a fraction. Use 48 for the numerator. The last digit of the decimal (the 8) is in the thousandths place, so use 1000 for the denominator. So the fraction is 48/1000. This reduces to a final answer of 6/125 (after dividing top and bottom each by 8).

For repeating decimals with infinitely many digits, there’s an algebra technique you will learn in 8th grade for converting to a fraction.(3 votes)

- your right he does say hundreds funny no offence(3 votes)
- When you have 76 hundredths and 6 is actually in the hundredths place then what is the place of the 70?(2 votes)
- The 0.70 part represents 70 hundredths, which is the same as 7 tenths.

So 0.76 can be thought of as 76 hundredths, or 7 tenths and 6 hundredths.

Have a blessed, wonderful day!(1 vote)

## Video transcript

- [Instructor] We are told
to write seven hundredths as a fraction and a decimal. Why don't you get some
paper and a pencil out and see if you can do that
before we do it together. All right, so let's do
it first as a fraction. So what is going to be the
denominator of our fraction if they're saying seven hundredths? And the way I'm saying it
is a little bit of a hint. Seven hundredths, oh, I
think you got the picture. We're dealing with hundredths. So our denominator is going to be 100. And then how many hundredths do we have? Well we have seven of them. I'll do that in a different
color just to be clear. We have seven of those hundredths. So there you have it, seven hundredths. That's this expressed as a fraction. Now what about as a decimal? Well, we could think
about our decimal places. If let's say that this is the ones place, and I'm just putting a little blank here. So this is the ones place, and you have a decimal right over here. And then this would be the tenths place. And then this would be
the hundredths place. Well we have, we want to
represent seven hundredths. So let me be clear, this
right over here is ones. This is tenths, and this is hundredths. I like saying, it's unusually
fun to say that, hundredths. All right, ones, tenths, hundredths. So how many ones do we have here? Well we have no ones, we have zero ones. How many tenths do we have here? Well we have no tenths. How many hundredths do we have? Well we have seven hundredths. Okay now it's getting annoying. We have seven hundredths. So you can write it that way as well. And if I wanted to just write
it a little bit cleaner, I could just write no ones, no
tenths, and seven hundredths. I said it the last time
like a normal person. Let's do another example. Here, we're told select the
written form of each number. And so they, on the left right over here, you have different representations here. We have things written
as a decimal, a fraction, another decimal, and
then we want to say hey, which of these are represented in words or a combination of
numbers and words up here. So pause this video and
have a go at this as well. Okay, so this first
number right over here, we have no ones, and
then as we go one space to the right of the decimal,
this is the tenths place. And it's clear we have
four of those tenths. So this right over here is four tenths. So that is this choice
right here, so we would, I'll shade it in, if you're
doing this on Khan Academy, you would just click there
and it would fill in. So what about this one? Well this one, we would read, you have four out of ten, or four tenths. So this again would be four tenths. So we would shade that one in. Now what's going on over here? We have no ones, we have no tenths. But we have four hundredths. I said it again, it's too much fun. So we have four hundredths. So that's this column. So we would fill that
one in, and we're done.