Place value is the value a digit has because of its position in a number. In 352, the 5 is in the tens place, so it is worth 50.

What is expanded form?

Expanded form writes a number as the sum of the values of its digits. For example, 4725 = 4000 + 700 + 20 + 5.

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

The place is the position, such as hundreds. The value is what the digit is worth there. In 4725 the 7 is in the hundreds place, and its value is 700.

Why is zero important in place value?

Zero holds a place that is empty. Without it, 405 and 45 would look the same. The 0 in 405 shows there are no tens.

What grade learns place value?

It runs right through elementary school. In the US Common Core, tens and ones come in grade 1, hundreds and expanded form in grade 2, numbers to 1,000,000 in grade 4 and decimals to thousandths in grade 5. In England it runs from Year 2 (tens and ones) to Year 6 (numbers to 10,000,000).

Are there free place value worksheets with answers?

Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Grades 2 to 5 (Years 3 to 6 in England)

Place value: what each digit is worth

Place value means a digit's value depends on where it sits: the 7 in 70 is worth ten times the 7 in 7. Here is how to read a number with a place value chart, write it in expanded form and avoid the usual slips. Try the free practice set below, then print fresh place value worksheets with an answer key.

The method, step by step

Name the places from the right: ones, tens, hundreds, then thousands, ten thousands, hundred thousands and so on.
Find the digit you are asked about and name its place.
Multiply the digit by its place value to find what it is worth: a 7 in the hundreds place is worth 7 × 100 = 700.
To write a number in expanded form, write the value of each non-zero digit and join them with plus signs.
Remember that a zero holds a place: it shows that place is empty, and it gets no part in expanded form.

CCSS 2.NBT.A.3CCSS 4.NBT.A.2CCSS 4.NBT.A.1England: Y2 Number and place valueEngland: Y3 Number and place valueEngland: Y4 Number and place valueEngland: Y5 Number and place value

Worked example

Write 40,382 in expanded form.

Put the digits in a place value chart, starting from the right: 2 ones, 8 tens, 3 hundreds, 0 thousands, 4 ten thousands.
Find each digit's value: 4 × 10,000 = 40,000, 3 × 100 = 300, 8 × 10 = 80 and 2 × 1 = 2.
The 0 in the thousands place is worth nothing, so it gets no part, but it still holds the place.
Check: 40,000 + 300 + 80 + 2 = 40,382.
40,382 = 40,000 + 300 + 80 + 2

Practice now

Question 1 of 100 correct

The value of 4 in 400 000 is how many times the value of 4 in 4000?

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Reading a place value chart

A place value chart has a column for each place. Reading from right to left, the columns are ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions. Each column is worth ten times the column to its right, so the chart is really the list 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000.

Charts for bigger numbers group the columns in threes: hundreds, tens and ones, then the same three for thousands, then for millions. That is where the commas in 6,480,175 come from. In that number the 7 is in the tens place, so it is worth 70, and the 4 is in the hundred thousands place, so it is worth 400,000.

Some books, and the practice questions on this page, group the digits with a small space instead of a comma, as in 6 480 175. It is the same number. The space avoids confusion in countries that use a comma as the decimal point.

Writing numbers in expanded form

Expanded form writes a number as the sum of what each digit is worth. 935 = 900 + 30 + 5, and 9348 = 9000 + 300 + 40 + 8. It turns a string of digits into the amounts they stand for, which is why it helps so much with adding, subtracting and rounding later on.

Zeros are where expanded form catches people out. 6072 is 6000 + 70 + 2, with no hundreds part. Going the other way, 500,000 + 3000 + 40 + 1 must be written 503,041, with zeros in the ten thousands and hundreds places.

Some teachers also use expanded notation, which shows the multiplication: 935 = 9 × 100 + 3 × 10 + 5 × 1. It is the same idea, written to show that each digit is multiplied by its place value.

Why each place is worth ten times the next

Our number system works in groups of ten. Ten ones make a ten, ten tens make a hundred and ten hundreds make a thousand. With base-ten blocks, a rod is ten cubes joined together and a flat is ten rods. Moving one place to the left multiplies a digit's value by 10.

That gives a handy check: the 9 in 9000 is worth 10 times the 9 in 900, and 100 times the 9 in 90. It also helps with counting whole groups. 3450 contains 34 whole hundreds, because 34 × 100 = 3400, with 50 left over.

Place value with decimals

The pattern carries on past the decimal point. The first place to the right of the point is tenths, then hundredths, then thousandths, each worth one tenth of the place to its left. In 9.817, the 8 is worth 8 tenths (0.8), the 1 is worth 1 hundredth (0.01) and the 7 is worth 7 thousandths (0.007).

So 9.817 in expanded form is 9 + 0.8 + 0.01 + 0.007. Notice there is no 'oneths' place. The pattern is balanced around the ones place, not around the decimal point: tens on one side of the ones, tenths on the other.

How it is taught in school

In the US, Common Core builds place value year by year. Grade 1 covers tens and ones (1.NBT.B.2). Grade 2 covers hundreds and reading and writing numbers to 1000 in expanded form (2.NBT.A.1, 2.NBT.A.3). Grade 4 extends this to whole numbers up to 1,000,000, including the idea that each place is worth ten times the place to its right (4.NBT.A.1, 4.NBT.A.2). Grade 5 adds decimals to thousandths (5.NBT.A.3).

In England, pupils recognize the value of each digit in two-digit numbers in Year 2, three-digit numbers in Year 3 and four-digit numbers in Year 4. Year 5 extends this to numbers up to at least 1,000,000 and Year 6 to 10,000,000, and by Year 6 pupils identify the value of each digit in decimals with three decimal places. Splitting a number into its parts, which UK teachers call partitioning, is the same idea as expanded form.

How parents can help

Build numbers with things you have at home, such as bundles of ten straws held with a rubber band. Coins work too: pennies, dimes and dollars are ones, tens and hundreds of cents.
Read big numbers aloud from the news or a map, then ask what one of the digits is worth.
Play 'make the biggest number': deal four digit cards and see who can arrange the largest and the smallest number.
Ask 'what is 10 more?' and 'what is 100 more?' to show that usually only one digit changes, then talk about what happens with 3495 + 10.
Print a fresh worksheet, mark it together with the answer key, and read the worked steps for any question that went wrong.

Common mistakes

Giving the digit instead of its value. In 979,930, the 7 is worth 70,000, not 7.
Leaving out zeros when writing a number from its parts. 4000 + 50 + 6 is 4056, not 456.
Writing expanded form with the digits only, such as 9 + 3 + 5 for 935. Each part must show what the digit is worth: 900 + 30 + 5.
Naming places from the left. Places are named from the right, starting with the ones, so the first digit of a long number could be in any place.
Thinking a decimal with more digits is bigger. 0.5 is greater than 0.45, because 5 tenths is more than 4 tenths.

Questions people ask

What is place value?: Place value is the value a digit has because of its position in a number. In 352, the 5 is in the tens place, so it is worth 50.
What is expanded form?: Expanded form writes a number as the sum of the values of its digits. For example, 4725 = 4000 + 700 + 20 + 5.
What is the difference between a digit's place and its value?: The place is the position, such as hundreds. The value is what the digit is worth there. In 4725 the 7 is in the hundreds place, and its value is 700.
Why is zero important in place value?: Zero holds a place that is empty. Without it, 405 and 45 would look the same. The 0 in 405 shows there are no tens.
What grade learns place value?: It runs right through elementary school. In the US Common Core, tens and ones come in grade 1, hundreds and expanded form in grade 2, numbers to 1,000,000 in grade 4 and decimals to thousandths in grade 5. In England it runs from Year 2 (tens and ones) to Year 6 (numbers to 10,000,000).
Are there free place value worksheets with answers?: Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated November 1, 2026.

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