Definition
Base-ten system
The base-ten system is a place-value system built from ten digits and groups of ten.
What it means
Think of each place as a box. Ten items in one box trade for one item in the box immediately to its left: 10 ones become 1 ten, and 10 tens become 1 hundred. The same pattern continues past the decimal point, where 10 tenths make 1 one.
Remember it
Move one place left: multiply by 10. Move one place right: divide by 10.
Example
In 4,372, the 4 is worth 4,000, the 3 is worth 300, the 7 is worth 70, and the 2 is worth 2. Moving the 7 one place left would make its value 700.
Watch for
Base ten is not the only possible number system; it is the positional system that groups place values by powers of ten.
Common mix-up
A digit is not always worth the same amount. In 505, the two 5s mean 500 and 5 because they sit in different places.
Exact meaning
The base-ten system uses the digits 0 through 9. A digit’s value depends on its place: one place to the left is worth ten times as much, and one place to the right is worth one tenth as much.