Place value
Type a number or add counters column by column. The number and its expanded form follow every change.
Settings
The chart
Use + and − under each column. With ten or more in a column, exchange ten of them for one in the next place up; break one back into ten in the place below.
The number:
Read the chart
Six charts with counters. Type the number each one shows; some have ten or more ones to exchange before you read them.
Use it in class
The worksheet and the board get exactly what is set now. You can edit the worksheet before printing, and its answer key comes on a separate page. On the board everything stays editable, and nothing is added to a live lesson.
How to use it
- Choose how many columns, from the ones up, then type a number or add counters.
- Put ten or more counters in a column and exchange ten of them for one in the next place up; break one into ten to take away across a place.
- For class: make an editable worksheet, with its answer key on a separate page, or put the chart on the board.
Worked examples
A chart with 14 in the tens
The chart has 3 hundreds, 14 tens and 2 ones. Ten of the tens make a hundred: exchange them, and the chart has 4 hundreds, 4 tens and 2 ones, which is 442.
Taking 7 from 52
52 has only 2 ones. Break one ten into ten ones: 4 tens and 12 ones. Take 7 ones away: 4 tens and 5 ones are left, which is 45.
Quick reference
- Each place is worth ten of the place after it: 1 ten = 10 ones, 1 hundred = 10 tens.
- A digit's value is the digit × the value of its place: in 352 the 5 is worth 50.
- Exchanging ten for one, or one for ten, changes how the number is shown, not the number.
You can type with either set of digits. The digit choice only changes how this tool shows numbers, and it is kept on this device. An operation written with ٠–٩ reads from right to left; one written with 0–9, from left to right.
Sources
Place value here is standard school arithmetic. The page computes every number and its expanded form itself, and automated tests check the exchanges.