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# Decimal place value

Sal introduces decimal numbers and understanding place value to the right of the decimal.

## Want to join the conversation?

- How do you divide a fraction?(54 votes)
- Let’s say you have a problem on your test that says 7/8 divided by 1/3.

First of all, let’s find out the reciprocal of 1/3. A reciprocal is a reversed fraction, so the reciprocal for 1/3 is 3/1.

Now you multiply 7/8 by 3/1.

To multiply a fraction, multiply numerator and demoninator, so 7/8 x 3/1 equals 21/8, which is an improper fraction. To make it proper, you must know how many times 8 fits into 21, which is 2, because 2 x 8 equals 16, but 3 x 8 equals 24, so it’s bigger than 21. Now we do 21 minus 16 to figure out the rest of the fraction. So we know that 21 - 16 = 5, and the denominator of 21/8 stays the same, so we have the mixed number 2 5/8.

So 7/8 divided by 1/3 equals 2 5/8.

*and also the video is about decimal place value and we are so off-topic right now 😅(41 votes)

- Why are decimals are so important and where and how do we use them?(11 votes)
- Decimals are important because as you get into more advanced math, you'll be finding squareroots of numbers that aren't even. Among other things along that line.(20 votes)

- Can there be negative decimals?(9 votes)
- Yes, we can attach a negative sign in front of any decimal to make it negative.

Have a blessed, wonderful day!(11 votes)

- is there such thing as oneths?(7 votes)
- No, once you have 10 tenths you will have 1 whole.

Just like if you were to go from 9 to 10. We would start at the ones place and move to the tens place by going up. The same thing will happen if we go down:

we start at 1 and go down instead of up but, we don't want to head into the negative part of the number line so we go to 1 tenths instead.

So, if you had oneths that would mean you have a whole number in the ones place.

So, there is no such thing as "oneths"(9 votes)

- what is a reciprocal?is it a fraction or a decimal?(7 votes)
- A reciprocal is like taking number 90 and adding one to the end like 190 and adding a slash in between the numbers like 1/90.

Take 5. Add 1 to the end to get 15. Add a slash: 1/5. Turn it into a decimal: 0.2, and there you have it. 1/2 equals 0.5, and 1/5 equals 0.2, crazy right!?(6 votes)

- i know what decimals are, but what can you do with them? all i know is that decimals are um instead of 235 your adding a decimal point and a 0.4 or 4/10 so its 235.4(6 votes)
- Everything to do with money uses decimals. So, you will be using them your entire life.(10 votes)

- How large can a decimal get?(7 votes)
- Like regular whole numbers it can be as small or as big as you want.

It can be 0.999999999999999999999999999999999999999999999999999999999999999999 and you can get as close to 1 as you want by adding more 9s. Or go really small and write something like 0.00000000000000000000000000000000000000000000000000000000000000000000001 and get closer to 0 by adding more 0s between the . and 1. A decimal can be any amount between 0 and 1.(5 votes)

- Why is there no oneth space in decimals?(5 votes)
- What you are calling the “oneths” place is really the units or ones place, which is the place immediately to the left of the decimal point.(7 votes)

- i'm confused on3:03(6 votes)
- I am at1:05and I am interested why he put this video which seems more of a introduction to decimals in the middle of the course?(6 votes)
- So I have a number written here. It's a 2, a 3, and a 5. And we already have some experience with numbers like this. We can think about 'what does it represent'. And to think about that we just have to look at the actual place values. So this right-most place right over here. This is the ones place. So this 5 represents five ones, or I guess you could say that's just going to be 5. This 3, this is in the tens place. This is the tens place, so we have three tens. So that's just going to be 30. And the 2 is in the hundreds place. So putting a 2 there means that we have two hundreds. So this number we can view as two hundred, thirty, five. Or you could view it as two hundred plus thirty plus five. Now what I want to do in this video is think about place values to the right of the ones place. And you might say 'wait, wait, I always thought that the ones place was the place furthest to the right.' Well everything that we've done so far, it has been. But to show that you can go even further to the right I'm going to put a little dot. I'm going to put a little dot right over here. We call that a 'decimal point'. And that dot means that anything to the right of this is going to be place values that are smaller, I guess you could say, than the ones place. So right to the left you have the ones place and the tens place and the hundreds place, and if you were to keep going you'd go to the thousands place and the ten thousands place. But then if you go to the right of the decimal point now you're going to divide by 10. So what am I talking about? Well, right to the right of the decimal point you are going to have-- find a new color-- this is going to be the tenths place. Well what does that mean? Well whatever number I write here that tells us how many tenths we're dealing with. So if I were to write the number 4 right over here, now my number is 2 hundreds plus 3 tens plus 5 ones plus 4 tenths. So you could view this a 4 times 1/10. Or you could write this as 4 tenths. Not tens, 4 tenths. Or 4 tenths is the same thing as this right over here. So this is a super important idea in mathematics. I can now use our place values to represent fractions. So this right over here, this 'point 4', this is 4/10. So another way to write this number-- I could write it this way, I could write it as two hundred, thirty-- let me do the thirty in blue-- two hundred and thirty five and four tenths. So I could write it like this, as a mixed number. So this up here would be a decimal representation: 235.4 And this right over here would be a mixed number representation: 235 and 4/10 but they all represent 200 plus 30 plus 5 plus 4/10. Let's look at a few more examples of this. So let's say I were to write the number 0.7-- and actually let me go one space even further to the right-- 0.76. So what would this be if I were to write it as a fraction? So let's just think about the place value. We have our decimal point. To the left of the decimal point is the ones place, but I have a zero there, so this is 0 ones. Now I have 7 tenths, so this is the tenths place. And then this is going to be this place to the right of that. We're going to divide by 10 again. So this is going to be the hundredths place. This space right over here is going to be the hundredths place. So this number right over here is-- we can rewrite it as 0-- let me write it this way-- we could rewrite it as 0 ones plus 7 tenths-- plus 7 tenths--- not tens, tenths-- plus 6 hundredths-- plus 6 hundredths-- not hundreds, hundredths. Or we could write this as 0 plus 7/10-- let me write that a little bit neater-- plus 7/10 plus 6/100-- 6 over 100. So you could write this-- 7/10 plus 6/100 is exactly what this is. You could say this is 0 ones, 7 tenths, and 6 hundredths. Now another way we could write this-- well look, if we wanted to write it as a fraction, or talk about it as a fraction-- I could ignore the 0, that's not going to change the value of the sum but I could add the 7/10 to the 6/100. So how could I write 7/10 in terms of hundredths? Well 7 over 10 is the same thing as 70 over 100. 7/10 is the same thing as 70 over 100. One way to thing about it is, if I multiply the denominator by 10 well, I can multiply the numerator by 10 as well and not change the value of it. 7/10 is the same thing as 70/100. And then you could add 6/100 to that-- 6/100 to that. And what will that give you? Well that's going to give you 76/100-- 76/100. So this number up here-- a lot of people will call this-- they might say 'zero point seven six' or they might call this 'seventy-six hundredths'. This is the hundredths place, this is the tenths place. But each tenth is worth ten hundredths. And you see that-- you could either view this as 7 tenths. or you could view it as 70 hundredths. So this is 76 hundredths. And you could keep going to the right. If you go to the right one more space you would get to the thousandths place and then the ten thousandths place. So you keep dividing by 10 each place you go to the right. And you multiply by 10 each place you go to the left.(1 vote)

## Video transcript

So I have a number written here. It's a 2, a 3, and a 5. And we already have some
experience with numbers like this. We can think about
'what does it represent'. And to think about that we just have
to look at the actual place values. So this right-most place right over here.
This is the ones place. So this 5 represents five ones, or I guess
you could say that's just going to be 5. This 3, this is in the tens place. This is
the tens place, so we have three tens. So that's just going to be 30. And the 2 is in the hundreds place. So putting a 2 there means
that we have two hundreds. So this number we can view as
two hundred, thirty, five. Or you could view it as
two hundred plus thirty plus five. Now what I want to do in this video
is think about place values to the right of the ones place.
And you might say 'wait, wait, I always thought
that the ones place was the place furthest to the right.' Well everything that we've done so far,
it has been. But to show that you can go
even further to the right I'm going to put a little dot. I'm going
to put a little dot right over here. We call that a 'decimal point'. And that dot means that anything
to the right of this is going to be place values that are smaller,
I guess you could say, than the ones place. So right to the left
you have the ones place and the tens place and
the hundreds place, and if you were to keep going
you'd go to the thousands place and the ten thousands place. But then if
you go to the right of the decimal point now you're going to divide by 10.
So what am I talking about? Well, right to the right of
the decimal point you are going to have-- find a new color-- this is going to be the tenths place. Well what does that mean? Well whatever number I write here that tells us how many tenths
we're dealing with. So if I were to write the number 4
right over here, now my number is 2 hundreds plus 3 tens plus 5 ones
plus 4 tenths. So you could view this a 4 times 1/10. Or you could write this as 4 tenths.
Not tens, 4 tenths. Or 4 tenths is the same thing as this
right over here. So this is a super important idea
in mathematics. I can now use our place values
to represent fractions. So this right over here, this 'point 4',
this is 4/10. So another way to write this number-- I could write it this way, I could write
it as two hundred, thirty-- let me do the thirty in blue-- two hundred
and thirty five and four tenths. So I could write it like this,
as a mixed number. So this up here would be a
decimal representation: 235.4 And this right over here would be a mixed number representation:
235 and 4/10 but they all represent 200
plus 30 plus 5 plus 4/10. Let's look at a few more examples of this. So let's say I were to write the number 0.7--
and actually let me go one space even further to the right-- 0.76. So what would this be if I were
to write it as a fraction? So let's just think about the place value. We have our decimal point. To the left of the decimal point
is the ones place, but I have a zero there,
so this is 0 ones. Now I have 7 tenths, so this is
the tenths place. And then this is going to be this place
to the right of that. We're going to divide by 10 again. So this is going to be the
hundredths place. This space right over here is
going to be the hundredths place. So this number right over here is--
we can rewrite it as 0-- let me write it this way-- we could
rewrite it as 0 ones plus 7 tenths-- plus 7 tenths--- not tens, tenths-- plus 6 hundredths-- plus 6 hundredths-- not hundreds, hundredths. Or we could write this as 0 plus 7/10-- let me write that a little bit neater--
plus 7/10 plus 6/100-- 6 over 100. So you could write this-- 7/10 plus
6/100 is exactly what this is. You could say this is 0 ones,
7 tenths, and 6 hundredths. Now another way we could
write this-- well look, if we wanted to write it as a fraction, or talk
about it as a fraction-- I could ignore the 0, that's not going to change the
value of the sum but I could add the 7/10 to the 6/100. So how could
I write 7/10 in terms of hundredths? Well 7 over 10 is the same thing as
70 over 100. 7/10 is the same thing as 70 over 100. One way to thing about it is, if
I multiply the denominator by 10 well, I can multiply the numerator by 10
as well and not change the value of it. 7/10 is the same thing as 70/100.
And then you could add 6/100 to that-- 6/100 to that.
And what will that give you? Well that's going to give you 76/100-- 76/100. So this number up here--
a lot of people will call this-- they might say
'zero point seven six' or they might call this
'seventy-six hundredths'. This is the hundredths place,
this is the tenths place. But each tenth is worth
ten hundredths. And you see that-- you could
either view this as 7 tenths. or you could view it
as 70 hundredths. So this is 76 hundredths. And you could keep going to the right. If you go to the right one more space you would get to the thousandths place and then the ten thousandths place. So you keep dividing by 10
each place you go to the right. And you multiply by 10
each place you go to the left.