Numbers & place value

Price tags, house numbers, game scores: numbers are everywhere, and you read them without thinking. Behind them sits a clever system that can write any number, however large, with just ten digits. Once you understand how it works, every number will instantly tell you a story.

The base ten system

We only have ten digits: 0 to 9. The trick is position. On the far right sit the ones, next to them the tens, then the hundreds and the thousands. Whenever ten of one kind come together, they become one unit of the next place: 10 ones make 1 ten, 10 tens make 1 hundred. So the number 352 contains 3 hundreds, 5 tens and 2 ones.

Position determines value

The same digit can mean very different things. The 7 in 74 stands for 70, the 7 in 47 for just 7. That's why comparing numbers is so easy: first check which number has more digits. If they have the same number of digits, compare from left to right, place by place. That's how you see at once that 98 is smaller than 189, even though the 9 up front looks so big. A zero at the very front does not count, though: 098 is exactly the same number as 98.

Reading big numbers

Even huge numbers are just places side by side. You read 4,052 like this: 4 thousands, 0 hundreds, 5 tens, 2 ones. The zero matters: it holds the hundreds place open so the 4 really means thousands. Without the zero it would say 452, a completely different number.