Place Value in Natural Numbers

Every digit in a number has a place value — its position tells you how much it is worth. Learn to read, write, and expand large numbers up to millions.

What Is Place Value?

In any number, each digit sits in a position — and that position decides how much the digit is worth. This is called place value.

Consider the number 47 356. Each digit has a different value depending on where it sits:

Position	Hundred-thousands	Ten-thousands	Thousands	Hundreds	Tens	Units
Digit	—	4	7	3	5	6
Value	—	40 000	7 000	300	50	6

Moving one position to the left makes a digit ten times bigger.

Note

In European number formatting, spaces separate groups of three digits: 1 000 000 (one million), 47 356 (forty-seven thousand three hundred and fifty-six). Never use commas for this purpose.

Place Value Positions

Here are the positions you need to know for 5th grade, from largest to smallest:

Position	Example digit in 3 748 502	Value
Millions	3	3 000 000
Hundred-thousands	7	700 000
Ten-thousands	4	40 000
Thousands	8	8 000
Hundreds	5	500
Tens	0	0
Units	2	2

Place Value Rule

\text{digit} \times \text{position value} = \text{digit's value}

Multiply the digit by its position value to find out how much it contributes to the whole number.

Expanded Form

Expanded form (also called expanded notation) shows a number as the sum of each digit's value. This makes place value very clear.

$47\,356 = 40\,000 + 7\,000 + 300 + 50 + 6$

$3\,748\,502 = 3\,000\,000 + 700\,000 + 40\,000 + 8\,000 + 500 + 0 + 2$

1
Identify each digit and its position
Read the number from left to right. Write down each digit and its position name.
2
Find the value of each digit
Multiply each digit by its position value. For example, the digit 4 in the ten-thousands place = 4 × 10 000 = 40 000.
3
Write the expanded form
Add all the values together with + signs: 40 000 + 7 000 + 300 + 50 + 6.
4
Check by adding
Add all the parts back together. The result should match the original number.

Write 205 060 in expanded form

Read the digits left to right:

2 is in the hundred-thousands place: $2 \times 100\,000 = 200\,000$
0 is in the ten-thousands place: $0 \times 10\,000 = 0$
5 is in the thousands place: $5 \times 1\,000 = 5\,000$
0 is in the hundreds place: $0 \times 100 = 0$
6 is in the tens place: $6 \times 10 = 60$
0 is in the units place: $0 \times 1 = 0$

$205\,060 = 200\,000 + 5\,000 + 60$

(Zeros do not need to be included in expanded form.)

Reading and Writing Numbers in Words

Large numbers are read in groups of three digits, right to left: units group, thousands group, millions group.

Number	In words
5	five
47	forty-seven
356	three hundred and fifty-six
7 000	seven thousand
47 356	forty-seven thousand three hundred and fifty-six
3 748 502	three million seven hundred and forty-eight thousand five hundred and two

Real world: city population

The population of a city is 385 720 people. Read this aloud:

385 is in the thousands group: "three hundred and eighty-five thousand"
720 is in the units group: "seven hundred and twenty"

Full reading: three hundred and eighty-five thousand seven hundred and twenty.

Real world: distance in kilometres

The distance from Earth to the Moon is approximately 384 400 km.

In expanded form: $384\,400 = 300\,000 + 80\,000 + 4\,000 + 400$

In words: three hundred and eighty-four thousand four hundred kilometres.

Real world: large sums of money

A school fundraiser raised 1 250 000 € (one million two hundred and fifty thousand euros).

Expanded form: $1\,250\,000 = 1\,000\,000 + 200\,000 + 50\,000$

Common Mistakes

Confusing the tens place and units place when a zero appears (e.g. writing 305 as 35)
Forgetting that zeros must hold a place — 4 007 is NOT the same as 47
Using commas as thousand separators (write 1 000 not 1,000)
Misreading the position of a digit in a large number — always count positions from the right
Skipping zeros in expanded form when they actually matter (they change the number)

Tip

To find a digit's place, count from the right starting at units (position 1), tens (position 2), hundreds (position 3), and so on.

Practice Problems

Write 63 084 in expanded form.

Show answer

60 000 + 3 000 + 80 + 4

What is the value of the digit 7 in the number 2 703 415?

Show answer

The digit 7 is in the hundred-thousands place. Its value is 7 × 100 000 = 700 000.

Write in digits: four hundred and six thousand and fifty.

Show answer

406 050