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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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# Decimals as words

Sal writes 0.17 and 40.03 in words. He also writes twenty-four hundredths using numbers.

## Want to join the conversation?

- What is the last place in decimal ?(54 votes)
- Ten thousandth.(21 votes)

- Is there such thing as millionths?(31 votes)
- Yup, there is such a thing. Like 190,000.123456(23 votes)

- Why isn't there a ones place in the decimal area?(21 votes)
- The decimal place values represent fractions. Any fraction with a denominator = 1 would still be a whole number.

5/1 = 5. 5 is a whole number so it is on the left of the decimal point.

Hope this helps.(23 votes)

- is there such thing as billionths?(14 votes)
- Yes, there are billionths!

0.1 = one tenth

0.01 = one hundredth

0.001 = one thousandth

0.0001 = one ten-thousandth

0.00001 = one hundred-thousandth

0.000001 = one millionth

...etc...

0.000000001 = one billionth

You could also write one billionth as a fraction, with**one billion**in the denominator:

1/1,000,000,000

Think of it like this: if you have 10 in the denominator, you have "tenths" and if you have 1000 in the denominator, you have "thousandths"

So in the same way, if you have 1,000,000,000 in the denominator, you have "billionths"

Hope this helps!(26 votes)

- I wonder... are there quadrillionths?(13 votes)
- For decimals, the quadrillionths place is the 15th position after the decimal point.(10 votes)

- is there such a thing as septillionths(8 votes)
- Yes, a septillionth exists and is equal to 1/1,000,000,000,000,000,000,000,000.

As a decimal, this is 0.000000000000000000000001.

In scientific notation (which you will learn about later), this is 10^(-24), meaning 10 to the -24 power.(13 votes)

- where are the onthes at(8 votes)
- It's impossible to have a oneths place because any number divided by 1 is just itself. It would still be a whole number.(9 votes)

- wait is there such a thing as sxadilionths(6 votes)
- Good question! I assume you mean sextillionths.

Yes, sextillionths exist. One sextillionth is the decimal point followed by twenty 0’s followed by a 1.(14 votes)

- how many decimals are there(4 votes)
- There is no limit to the number of decimal digits that can be used. For example: 0.000000007 = 7 billionths, a very small fractional value. There are also repeating decimals where the decimal digits never end.(14 votes)

- how do you put billions in decimals(8 votes)

## Video transcript

- [Voiceover] Let's say
that I had the number zero point one seven. How could I say this number? I said it one way, I said
zero point one seven, but what are other ways
that I could say it, especially if I wanted to express it in terms of tenths or hundredths or other places? And like always, try to pause the video and try think about it on your own. Alright, so there's
actually a couple of ways that we could say this number. One is just to say zero point one seven. Other ways are to say look, I have a one in the tenths place, so that's going to be one tenth, one tenth and one tenth and I have a seven
in the hundredths place, so this is a seven right over here in the hundredths place, so I can say one tenth and seven hundredths. Hun- Hundredths. And there you go. That's one way to say this number. Now another to think about it is just say the whole thing
in terms of hundredths. So a tenth is how many hundredths? Well a tenth is the same
thing as 10 hundredths, so you could say, you could say instead of a tenth, you could
say this is 10 hundredths, and the way I'm writing it right now, very few people would
actually do it this way. 10 hundredths and and seven hundredths. And seven hundredths. Well not I could just
add these hundredths, if I have 10 hundredths and I have another seven hundredths, that's
going to be 17 hundredths. So I could just write this down as 17 hundredths. Hundredths. And to make that intuition of how we could just call this 17
hundredths instead of just calling it one tenth and seven hundredths, let's actually count by hundredths. So that is one hundredth, that is two hundredth, and actually, let me just go straight to nine hundredths. So I skipped a bunch right over here. And what would be the
next, how would I say 10 hundredths? Well 10 hundredths, let
me write it this way, 10 hundredths is the
same thing as one tenth. So if we go from nine
hundredths, the next, if I'm counting by hundredths,
the next one's going to be 10 hundredths. Now once again, 10
hundredths is the same thing as one tenth, just the
same way that 10 ones is the same thing as one 10. I hope that doesn't confuse you, but we could keep counting. 10 hundredths, 11 hundredths, 12 hundredths, 13 hundredths, 14 hundredths, 15 hundredths, 16 hundredths, and then
finally 17 hundredths. So hopefully that gives
you a little intuition for why we can call this number, instead of just calling
it zero point one seven, or one tenth and seven hundredths, we could call this 17 hundredths. So with that out of the way,
let's do a couple of examples going the other way. Let's say we're given a name of a number or the words, and we wanna
write it down as a decimal. So this is four tens and three hundredths. Alright, so four tens. So the four tens right over here. So actually let me just
put some places over here, so this would be, if
this is our tens place, and then this is our ones place, and then you're gonna have your decimal, and then you're gonna
have your tenths place, tenths place, and then
you're going to have, and I'll do this in a different color, your hundredths place. Hun- Hundredths place. So we're going to have four tens. Not tenths, four tens. So four tens, zero ones, zero ones, we got our decimal, they don't have any tenths
over here so zero tenths, and then we have three hundredths. Three hundredths, so three hundredths. So four tens, which is
the same thing as 40, and three hundredths right over here, so 40 point zero three. Let's do another one of
these, this is kinda fun. So we have 24 hundredths. 24 hundredths. So by the logic that we
saw in the first one, in the first one, we
could just write this as, remember, this would be nine hundredths, and if we want one more hundredth, this would be 10 hundredths. So if we want to do 24 hundredths, it would just be zero point two four. And if you're saying well wait a minute, this looks like two tenths
and four hundredths, you'd be right! But remember, so actually let
me, I could re-write this as, I could re-write this as two tenths, two tenths and four hundredths. Let me say and four hundredths. Hundredths. But remember, a tenth is
equal to 10 hundredths, so two tenths is the same
thing as 20 hundredths. Hundredths. I have trouble saying- So this is the same thing as 20 hundredths and four hundredths. And four, let me write it neatly. Four hundredths. And of course 20 hundredths
and four hundredths is the same thing as 24 hundredths. So hopefully that makes sense.