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## Numbers & Operations - The Real & Complex Number Systems 211-217

### Course: Numbers & Operations - The Real & Complex Number Systems 211-217 > Unit 1

Lesson 3: Decimals in expanded form# Write decimals in expanded form

To write a decimal in expanded form, we need to break down each digit according to its place value. Start with the whole number portion, identifying the hundreds, tens, and ones places. Then, move on to the tenths, hundredths, and thousandths places. Keep in mind the order of operations when combining the expanded terms. Created by Sal Khan.

## Want to join the conversation?

- Why did you say point on this video instead of saying and?The right way to say a decimal is and.(108 votes)
- Either way is correct. Generally when you write decimals out in words you will say "and", and when you write them in numbers you will say "point".(153 votes)

- Why the left side of decimal is once and other right side is tenths(7 votes)
- because there are such a thing as a ones digit (1,2,3,4,5,6,7,8,9), but there is no such thing as a oneths digit. .1 = 1/10 (one tenth) .2 = 2/10 (two tenths) etc.(15 votes)

- how do you even make a project?(5 votes)
- Do you mean a coding project? If it's a coding project then you can create a new one with this link: https://www.khanacademy.org/computer-programming/new/pjs

Or you can create a spin-off of a project (basically a your version of a game that's already created).

https://www.khanacademy.org/computer-programming/harry-and-rese/4773334497181696

https://www.khanacademy.org/computer-programming/the-current/6413308542713856

https://www.khanacademy.org/computer-programming/gravity-ft-platformerking/5231693312507904

You can create a spin-off from those links above.(10 votes)

- Why when you did the seven hundredth you put it in a fraction. Why is that(3 votes)
- Because decimals are a fraction. In expanded form, we write each digit with its corresponding place value. All the decimal digits have place values that are fractions.(6 votes)

- why does he do the digits in dif colors?(4 votes)
- I think it's to represent each value maybe?(4 votes)

- I do not get what you are talking about because it is confusing brake it down easyer(5 votes)
- i'm finding this complicated with all those numbers, is there an easier way to remember or to understand it?(5 votes)
- Absolutely. If you don't understand the words break them down into smaller words and if you don't understand the math you could watch the video a few times and you will probably get it. If you don't reach out again and someone will be able to help you(1 vote)

- I don’t understand(4 votes)
- can a decimal go forever(2 votes)
- Yes, it can. They are called non-terminating decimals. An example is pi, mathematicians are still trying to find the end, if there is one. Also, if there is a number that is like 3.66666666666666666666, you can put a bar notation over the first 6.(4 votes)

- is a decimal point the same thing as the word "and"?(5 votes)

## Video transcript

Let's say I have
the number 905.074. So how could I expand this out? And what does this
actually represent? So let's just think about
each of the place values here. The 9 right over here, this
is in the hundreds place. This literally
represents nine hundreds. So we could rewrite
that 9 as nine hundreds. Let me write it two ways. We could write it
as 900, which is the same thing as 9 times 100. Now, there's a 0. That's just going to
represent zero tens. But zero tens is still just 0. So we don't have to
really worry about that. It's not adding any value to
our expression or to our number. Now we have this 5. This 5 is in the ones place. It literally
represents five ones, or you could just
say it represents 5. Now, if we wanted to
write it as five ones, we could say well, that's
going to be 5 times 1. So far, we've represented
905, 900 plus 5 or 9 times 100 plus 5 times 1. And you might say
hey, how do I know whether I should
multiply or add first? Should I do this addition
before I do this multiplication? And I'll always remind
you, order of operations. In this scenario, you would
do your multiplication before you do your addition. So you would multiply your 5
times 1 and your 9 times 100 before adding these
two things together. But let's move on. You have another 0. This 0 is in the tenths place. This is telling us the number
of tenths we're going to have. This is zero tenths, so
it's really not adding much, or it's not adding anything. Now we go to the
hundredths place. So this literally
represents seven hundredths. So we could write this as
7/100, or 7 times 1/100. And then finally, we go
to the thousandths place. So we go to the
thousandths place. And we have four thousandths. So that literally represents 4
over 1,000, or 4 times 1/1000. Notice this is coming
from the hundreds place. You have zero tens, but I'll
write the tens place there just so you see it. So it's zero tens, so I didn't
even bother to write that down. Then you have your ones place. You have five ones. Then you have zero tenths. So I didn't write that down. Then you have seven
hundredths and then you have four thousandths. And we are done. We've written this out,
really just understanding what this number represents.