Free printable place value chart
Grades K–4Millions down to hundredths on one sheet, with expanded form, word form and what each digit is actually worth. Print it for the wall, or type a number into the live chart below and watch it come apart.
Tap the chart to open it at full size
Place value chart, millions to hundredths
The printed chart carries this layout. Here it is live: type any number into the box, or tap one of the examples, and it drops into the right columns.
Tap a column to find out what that digit is worth. The 2 in 5,283.47 is not a 2 — it is two hundred, because of where it is sitting. That single idea is the whole of place value, and it is the reason the same ten digits can write every number there is.
Try 7, then 40, then 306. Watch where the zero goes in 306 and why it has to be there at all: it is holding the tens place open so the 3 stays in the hundreds. A child who understands that one zero has understood most of what this chart teaches.
| Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones | Tenths | Hundredths | |
|---|---|---|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 | · | 0.1 | 0.01 |
| 0 | 0 | 0 | 5 | 2 | 8 | 3 | . | 4 | 7 |
- Expanded form
- 5,000 + 200 + 80 + 3 + 0.4 + 0.07
- Word form
- Five thousand, two hundred eighty-three and forty-seven hundredths
Tap any column to see what that digit is worth.
How to use this place value chart at home
Start with the columns empty and fill them together. Say a number aloud, let the child place each digit, then read back what each one is worth. Doing it in that order — hear it, place it, value it — is what separates place value from copying digits into boxes.
Then go the other way. Point at a digit and ask what it is worth rather than what it is. The answer to "what is this digit" is four; the answer to "what is it worth" is four hundred. Children who can only answer the first question have not got place value yet, however neat their handwriting is.
Come back to it whenever regrouping goes wrong. Almost every stubborn error in column addition, subtraction, rounding and decimals is a place value error underneath. Rather than reteaching the algorithm, put the number in the chart and ask what the digits are worth.
Why this is the chart to print first
Of everything in this library, place value is the one that the most other topics lean on. Carrying a ten in addition is place value. Borrowing in subtraction is place value. Rounding to the nearest hundred is a question about which column you are looking at. Decimals are the same columns continued past the point, and long multiplication's shifted second line is place value too.
That makes it unusually good value for wall space. A chart that only helps with one topic comes down after a few weeks; this one keeps earning its place from Kindergarten through Grade 5, which is why it is worth printing on decent paper.
The three forms of the same number
Standard form is the way numbers are normally written: 5,283. It is compact and it hides everything about how it works.
Expanded form pulls it apart: 5,000 + 200 + 80 + 3. This is where a child can see that the 2 is worth two hundred, and it is the form that makes regrouping obvious rather than magical. If a child cannot write expanded form, column addition will stay a procedure they follow rather than something they understand.
Word form is how you say it: five thousand, two hundred eighty-three. It matters more than it looks, because word problems and instructions are written in it, and because the way English names numbers gives away the structure. Five thousand, two hundred — the words are the columns, in order.
Where place value usually goes wrong
Dropping the placeholder zero. Asked to write three hundred six, the child writes 36. They heard three hundred and they heard six and they wrote both, and nothing in what they heard mentioned the tens. This is a listening-to-structure problem, and putting it in the chart fixes it faster than correcting it does.
Reading digits instead of values. Answering "four" when asked what the 4 in 47 is worth. It sounds like a quibble and it is not — a child who cannot say forty will not understand why the 4 moves when you regroup.
Comparing numbers by length once decimals arrive. Believing 0.45 is bigger than 0.7 because it has more digits. This is the commonest decimal error there is, and it comes from applying a whole-number rule that used to work. Lining both up in the chart makes it visible immediately.
Losing the alignment in written work. Numbers written with the digits out of column produce wrong answers even when every fact is known. Squared paper, or a printed copy of this chart to write straight into, removes most of it.
After the chart goes up
A chart explains the idea but gives a child nothing to do. These do the rest.
- place value at Mathify Kids — every topic in this area, sorted by grade.
- comparing numbers worksheets — printable practice.
- rounding numbers worksheets — the next step once this is solid.
- multiply by 10 100 1000 worksheets — more practice in the same area.
Everything at this level: Kindergarten math · Grade 1 math · Grade 2 math · Grade 3 math · Grade 4 math
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Questions parents ask
What is place value?
The idea that a digit's value depends on where it sits. The 4 in 47 means forty; the 4 in 4.7 means four. Ten digits and a set of positions are enough to write every number there is, which is a genuinely remarkable thing and worth saying out loud to a child at least once.
How do you use a place value chart?
Write the number into the columns, one digit per column, lining the ones digit up with the ones column. Then read off what each digit is worth by looking at the heading above it. The live chart above does this automatically — type a number and it lands in the right places.
What is expanded form?
The number written as the sum of what each digit is worth. 5,283 in expanded form is 5,000 + 200 + 80 + 3. It is the clearest way to show a child that the digits are not just characters in a row, and it is what makes regrouping in addition and subtraction make sense later.
Why do we need zero as a placeholder?
Because without it the columns collapse. In 306 the zero holds the tens place open so the 3 stays in the hundreds; take it out and you have 36, a completely different number. Children who drop placeholder zeros are not being careless — they have not yet seen that the zero is doing a job.
What grade is this place value chart for?
Kindergarten through Grade 4 for the whole-number columns, with decimals usually arriving in Grade 4 or 5. It is probably the single most useful chart to print first, because addition regrouping, subtraction borrowing, rounding and decimals all rest on it.
Is this place value chart free to print?
Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.
How should I print it so the numbers are readable?
Print at 100% scale rather than Fit to page, match the orientation to the chart's shape, and turn off headers and footers. Printing a copy per child for a math folder works well here, because place value gets written into rather than just read.