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Writing a Number in Expanded Form (Place value) - Arithmetic Properties
FAQs on Writing a Number in Expanded Form (Place value) - Arithmetic Properties
| 1. What is expanded form in place value? |  |
Expanded form in place value is a way of representing a number by showing the value of each digit in the number according to its place value. It involves breaking down the number into its individual place values and adding them together. For example, the expanded form of the number 456 would be 400 + 50 + 6.
| 2. How can I write a number in expanded form? | |
To write a number in expanded form, you need to identify the place value of each digit in the number. Start from the leftmost digit and determine its value based on its position. Then, write each digit's value with its corresponding place value. Finally, add all the values together. For example, to write the number 842 in expanded form, you would have 800 + 40 + 2.
| 3. Why is expanded form important in mathematics? | |
Expanded form is important in mathematics as it helps students understand the concept of place value and the value of each digit in a number. It allows them to break down numbers into their individual parts, making it easier to perform operations like addition and subtraction. It also helps in developing a deeper understanding of the number system.
| 4. Can expanded form be used for decimal numbers? | |
Yes, expanded form can also be used for decimal numbers. In the expanded form of a decimal number, each digit is written with its corresponding place value, just like in whole numbers. For example, the expanded form of the decimal number 6.25 would be 6 + 0.2 + 0.05.
| 5. How does expanded form relate to word form and standard form? | |
Expanded form, word form, and standard form are all different ways of representing numbers. Expanded form shows the value of each digit in a number according to its place value. Word form represents a number using words, such as "five hundred twenty-seven". Standard form is the normal way of writing a number, using digits without any additional notation. These different forms help in understanding and communicating numbers in various ways.
Text Transcript from Video
Write 14,897 in expanded form.
Let me just rewrite the number,
and I'll color code
it, and that way, we can keep
track of our digits.
So we have 14,000.
I don't have to write
it-- well, let me
write it that big.
14,000, 800, and 97-- I already
used the blue; maybe I
should use yellow--
in expanded form.
So let's think about
what place each of
these digits are in.
This right here, the 7,
is in the ones place.
The 9 is in the tens place.
This literally represents 9
tens, and we're going to see
this in a second.
This literally represents
7 ones.
The 8 is in the hundreds
place.
The 4 is in the thousands
place.
It literally represents 4,000.
And then the 1 is in the
ten-thousands place.
And you see, every time you move
to the left, you move one
place to the left, you're
multiplying by 10.
Ones place, tens place, hundreds
place, thousands
place, ten-thousands place.
Now let's think about what
that really means.
If this 1 is in the
ten-thousands place, that
means that it literally
represents-- I want to do this
in a way that my arrows
don't get mixed up.
Actually, let me start
at the other end.
Let me start with what
the 7 represents.
The 7 literally represents
7 ones.
Or another way to think about
it, you could say it
represents 7 times 1.
All of these are equivalent.
They represent 7 ones.
Now let's think about the 9.
That's why I'm doing it from the
right, so that the arrows
don't have to cross
each other.
So what does the 9 represent?
It represents 9 tens.
You could literally imagine
you have 9 actual tens.
You could have a 10, plus
a 10, plus a 10.
Do that nine times.
That's literally what it
represents: 9 actual tens.
9 tens, or you could say it's
the same thing as 9 times 10,
or 90, either way you want
to think about it.
So let me write all
the different ways
to think about it.
It represents all of these
things: 9 tens, or 9
times 10, or 90.
So then we have our 8.
Our 8 represents-- we see it's
in the hundreds place.
It represents 8 hundreds.
Or you could view that as being
equivalent to 8 times
100-- a hundred, not
a thousand-- 8
times 100, or 800.
That 8 literally represents
8 hundreds, 800.
And then the 4.
I think you get the idea here.
This represents the
thousands place.
It represents 4 thousands, which
is the same thing as 4
times 1,000, which is the
same thing as 4,000.
4,000 is the same thing
as 4 thousands.
Add it up.
And then finally, we have this
1, which is sitting in the
ten-thousands place, so it
literally represents 1
ten-thousand.
You can imagine if these were
chips, kind of poker chips,
that would represent one of the
blue poker chips and each
blue poker chip represents
10,000.
I don't know if that
helps you or not.
And 1 ten-thousand is the same
thing as 1 times 10,000 which
is the same thing as 10,000.
So when they ask us to write it
in expanded form, we could
write 14,897 literally as the
sum of these numbers, of its
components, or we could
write it as the
sum of these numbers.
Actually, let me write this.
This top 7 times 1 is
just equal to 7.
So 14,897 is the same thing as
10,000 plus 4,000 plus 800
plus 90 plus 7.
So you could consider this
expanded form, or you could
use this version of it, or you
could say this the same thing
as 1 times 10,000, depending on
what people consider to be
expanded form-- plus 4 times
1,000 plus 8 times 100 plus 9
times 10 plus 7 times 1.
I'll scroll to the right
a little bit.
So either of these could be
considered expanded form.
Let me just rewrite the number,
and I'll color code
it, and that way, we can keep
track of our digits.
So we have 14,000.
I don't have to write
it-- well, let me
write it that big.
14,000, 800, and 97-- I already
used the blue; maybe I
should use yellow--
in expanded form.
So let's think about
what place each of
these digits are in.
This right here, the 7,
is in the ones place.
The 9 is in the tens place.
This literally represents 9
tens, and we're going to see
this in a second.
This literally represents
7 ones.
The 8 is in the hundreds
place.
The 4 is in the thousands
place.
It literally represents 4,000.
And then the 1 is in the
ten-thousands place.
And you see, every time you move
to the left, you move one
place to the left, you're
multiplying by 10.
Ones place, tens place, hundreds
place, thousands
place, ten-thousands place.
Now let's think about what
that really means.
If this 1 is in the
ten-thousands place, that
means that it literally
represents-- I want to do this
in a way that my arrows
don't get mixed up.
Actually, let me start
at the other end.
Let me start with what
the 7 represents.
The 7 literally represents
7 ones.
Or another way to think about
it, you could say it
represents 7 times 1.
All of these are equivalent.
They represent 7 ones.
Now let's think about the 9.
That's why I'm doing it from the
right, so that the arrows
don't have to cross
each other.
So what does the 9 represent?
It represents 9 tens.
You could literally imagine
you have 9 actual tens.
You could have a 10, plus
a 10, plus a 10.
Do that nine times.
That's literally what it
represents: 9 actual tens.
9 tens, or you could say it's
the same thing as 9 times 10,
or 90, either way you want
to think about it.
So let me write all
the different ways
to think about it.
It represents all of these
things: 9 tens, or 9
times 10, or 90.
So then we have our 8.
Our 8 represents-- we see it's
in the hundreds place.
It represents 8 hundreds.
Or you could view that as being
equivalent to 8 times
100-- a hundred, not
a thousand-- 8
times 100, or 800.
That 8 literally represents
8 hundreds, 800.
And then the 4.
I think you get the idea here.
This represents the
thousands place.
It represents 4 thousands, which
is the same thing as 4
times 1,000, which is the
same thing as 4,000.
4,000 is the same thing
as 4 thousands.
Add it up.
And then finally, we have this
1, which is sitting in the
ten-thousands place, so it
literally represents 1
ten-thousand.
You can imagine if these were
chips, kind of poker chips,
that would represent one of the
blue poker chips and each
blue poker chip represents
10,000.
I don't know if that
helps you or not.
And 1 ten-thousand is the same
thing as 1 times 10,000 which
is the same thing as 10,000.
So when they ask us to write it
in expanded form, we could
write 14,897 literally as the
sum of these numbers, of its
components, or we could
write it as the
sum of these numbers.
Actually, let me write this.
This top 7 times 1 is
just equal to 7.
So 14,897 is the same thing as
10,000 plus 4,000 plus 800
plus 90 plus 7.
So you could consider this
expanded form, or you could
use this version of it, or you
could say this the same thing
as 1 times 10,000, depending on
what people consider to be
expanded form-- plus 4 times
1,000 plus 8 times 100 plus 9
times 10 plus 7 times 1.
I'll scroll to the right
a little bit.
So either of these could be
considered expanded form.
About this Video
Apr 20, 2026 Last updated
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