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### Unit 14: Lesson 45

Decimals in expanded form# Write decimal in expanded form

CCSS.Math: ,

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.

## 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.