Place Value Calculator
Enter a number and this breaks it into digits, naming the column each one sits in and what it is worth there.
Place value of
4,703
- The 4 is in the thousands
- worth 4,000
- The 7 is in the hundreds
- worth 700
- The 0 is in the tens
- worth 0
- The 3 is in the ones
- worth 3
- Expanded form: 4,000 + 700 + 3.
- In words: Four thousand seven hundred and three.
- A digit has two different values. Its face value is just the digit itself; its place value is what it is worth where it sits. Those are the two words the question is usually asking you to tell apart.
- Each column is ten times the one to its right, which is what makes this a base ten system and why a zero has to be written even when there is nothing in that column.
About place value
Every digit has two different values and the exercise is almost always testing whether you can tell them apart. Its face value is just the digit itself. Its place value is what it is worth where it sits. In 4,703 the 7 has a face value of 7 and a place value of 700.
The columns work in powers of ten, each one worth ten times the column to its right: ones, tens, hundreds, thousands and so on. That is what makes this a base ten system, and it is the reason a number can be written with only ten symbols however large it gets.
It is also why zero has to be written even when there is nothing in that column. The 0 in 4,703 is not decoration — it holds the tens column open so the 7 stays in the hundreds. Take it out and you have 473, a completely different number. That role, as a placeholder rather than as a quantity, is the whole reason zero was such a difficult idea historically.
Expanded form writes the number as the sum of its place values: 4,000 + 700 + 3. It looks like busywork and is not, because it makes the structure visible and it is what column addition, subtraction and long multiplication all quietly rely on.
What it works out
- The place value of every digit
- The name of each column
- Expanded form
- The number written out in words
The formula
Place value = Digit × (10 raised to its position from the right)
Count the columns from the right, starting at zero. The rightmost is the ones column, worth 10 to the power 0, which is 1. Next is the tens, worth 10. Then the hundreds, worth 100, and so on.
In 4,703 the 4 sits three places from the right, so it is worth 4 × 1,000 = 4,000. The 7 sits two places from the right, worth 7 × 100 = 700. The 0 is worth 0 × 10 = 0. The 3 is worth 3 × 1 = 3.
Adding those back gives the expanded form: 4,000 + 700 + 3 = 4,703.
The zero contributes nothing to the total and everything to the arrangement. Without it the 7 would slide into the tens column and the number would read 473. That is why a placeholder zero is written and why it can never simply be dropped.
- Face value
- The digit on its own, ignoring where it is.
- Place value
- What the digit is worth in the column it occupies.
- Column
- Each one is ten times the one to its right — ones, tens, hundreds, thousands.
A worked example
The number 4,703 broken into its place values.
That works out to 4,703 .
- The 4 is in the thousands
- worth 4,000
- The 7 is in the hundreds
- worth 700
- The 0 is in the tens
- worth 0
- The 3 is in the ones
- worth 3
Questions
What is place value?
What a digit is worth because of where it sits in a number. The 7 in 4,703 has a place value of 700, because it is in the hundreds column.
What is the difference between face value and place value?
Face value is the digit itself; place value is what it is worth where it is. In 4,703 the 7 has a face value of 7 and a place value of 700. This is what most place value questions are really asking.
What is expanded form?
A number written as the sum of its place values. 4,703 in expanded form is 4,000 + 700 + 3.
Why do we need zero in a number?
To hold a column open. The 0 in 4,703 keeps the 7 in the hundreds; remove it and you get 473. Zero as a placeholder is what makes a positional number system possible at all.
What are the column names in order?
From the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions. Each is ten times the one before it.
What is the place value of a digit after the decimal point?
The columns keep going, dividing by ten each time: tenths, hundredths, thousandths. The 7 in 0.07 has a place value of seven hundredths.
Why does place value matter?
Because column addition, subtraction, long multiplication and long division all depend on it. Carrying and borrowing are place value operations, and mistakes in them are usually place value mistakes.
What is the largest place value in 4,703?
The thousands, held by the 4, which is worth 4,000. The leftmost digit always carries the largest place value.