The same digit can be worth different amounts
Look at the number 345. It has three digits, and each one has a place:
- The 5 is in the ones place. It is worth 5.
- The 4 is in the tens place. It is worth 4 tens, which is 40.
- The 3 is in the hundreds place. It is worth 3 hundreds, which is 300.
Put them together: 300 + 40 + 5 = 345. A 3 at the front of 345 is worth far more than a 3 at the end of 543. The place decides the value.
Each place is ten times bigger
Ten ones make one ten. Ten tens make one hundred. Ten hundreds make one thousand. Every step to the left is ten times bigger than the step before it.
Think of money. Ten pennies are worth one dime. Ten dimes are worth one dollar.
What zero is for
Zero holds a place open. In 305 there are 3 hundreds, no tens, and 5 ones. Without the zero it would read 35, which is a different number. Zero means "nothing in this place," and it keeps the other digits where they belong.
Why carrying works
Add 27 + 15. Start with the ones: 7 + 5 = 12. But 12 is too many to fit in the ones place, because 12 is really 1 ten and 2 ones.
So write the 2 in the ones place and move the 1 ten over to the tens place. That is "carrying the one." Now add the tens: 2 + 1 + 1 = 4 tens. The answer is 42.
You are not carrying a 1. You are moving one whole ten to where the tens live.
Why borrowing works
Borrowing is the same trade in reverse. When you need more ones, you break a ten into ten ones. Our page on subtraction in plain English walks through an example.
Reading bigger numbers
After hundreds come thousands. In 2,468 there are 2 thousands, 4 hundreds, 6 tens and 8 ones. The comma is just there to make long numbers easier to read. It splits the digits into groups of three.
See it with real things
Use dimes and pennies. Show 34 as 3 dimes and 4 pennies. Add 8 more pennies and you'll have 12 pennies. Swap ten of them for a dime. Now you have 4 dimes and 2 pennies: 42. You just carried.
A ten-frame mat or hundred chart shows the same thing on paper.
Practice without anyone watching
Fun With Learning is a free app with no ads and nothing to buy. Block Builder shows tens and ones as blocks, and Carry the One shows the carried ten moving up the column. There are no timers. See the math games and activities.
