What Is Place Value? Digits, Base Ten and Expanded Form

Q: What is the difference between a digit's face value and its place value?

The face value is just the digit itself, such as 7. Its place value, or value in the number, is the digit multiplied by its position, so the 7 in 4372 is worth 70.

Why the 3 in 4372 is worth 300, how base ten works, and how writing a number in expanded form makes every later method, from column addition to decimals, make sense.

4 min read Supports 3 lessons

We write every whole number with just ten symbols: $0, 1, 2, \dots, 9$ . The trick that lets ten symbols describe numbers as large as you like is position. The same digit means something different depending on where it sits.

Take the $3$ in $4372$ and the $3$ in $3$ . They look identical, but one is worth three hundred and the other is worth three. That difference is place value.

4thousands×1,000

3hundreds×100

7tens×10

2ones×1

Each column is worth ten times the column to its right.

Why it is called base ten

Count objects one at a time and, as soon as you reach ten, bundle them into a single ten. Ten tens make a hundred, ten hundreds make a thousand, and so on. Every column holds how many bundles of that size you have, and no column ever needs more than nine.

Because each bundle is ten of the one before, our system is called base ten (or the decimal system, from the Latin decem, ten).

1 \xrightarrow{\times 10} 10 \xrightarrow{\times 10} 100 \xrightarrow{\times 10} 1000 \xrightarrow{\times 10} 10\,000

Moving one place left multiplies a digit's value by ten.

Expanded form

Writing a number as the sum of what each digit is worth is called expanded form. It turns place value from an idea into something you can see and calculate with.

$4372$
Start with the number as we normally write it.

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Key idea

A digit's value is digit × place value. In $85{,}196$ the $5$ is in the thousands place, so it is worth $5 \times 1000 = 5000$ .

The role of zero

Zero is what makes the system work. In $405$ , the $0$ says there are no tens. Without it, $405$ and $45$ would look the same. A zero that holds a place open like this is called a placeholder.

Watch out

Zeros inside a number matter; zeros at the very front do not. $0405$ is still $405$ , but $4050$ is ten times bigger than $405$ .

Why place value matters later

Almost every written method relies on it. Column addition lines digits up by place so that ones are added to ones and tens to tens. Multiplying by $10$ shifts every digit one place left. Decimals simply carry the pattern on to the right of the units, where each place is a tenth of the one before it.

Worked example

What is the value of the $6$ in $2{,}063{,}914$ ?

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Count places from the right: ones, tens, hundreds, thousands, ten-thousands.

Tip

When numbers get long, group the digits in threes from the right: $2{,}063{,}914$ . Each group of three is a new name: thousands, then millions.

Common questions

What is the difference between a digit's face value and its place value?: The face value is just the digit itself, such as $7$ . Its place value, or value in the number, is the digit multiplied by its position, so the $7$ in $4372$ is worth $70$ .
Is place value only for whole numbers?: No. The same pattern continues to the right of the decimal point: tenths, hundredths, thousandths. Each place is still a tenth of the place to its left.

Practise place value

The Place Value lesson has worked examples and unlimited practice that adapts to you.

Open the lesson

Common questions

What is the difference between a digit's face value and its place value?

The face value is just the digit itself, such as $7$ . Its place value, or value in the number, is the digit multiplied by its position, so the $7$ in $4372$ is worth $70$ .

Is place value only for whole numbers?

No. The same pattern continues to the right of the decimal point: tenths, hundredths, thousandths. Each place is still a tenth of the place to its left.