Place value is the system that gives a digit different meanings depending on where it sits in a number. In the number 222, each 2 means something different: the first 2 means two hundred, the middle 2 means twenty, and the last 2 means two. The position of each digit determines its value.

This system makes our number system incredibly powerful. Instead of needing separate symbols for every possible number (imagine having unique symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and on and on forever!), we can write any number using just ten digits: 0 through 9.

Each position represents a power of ten. Moving one place to the left multiplies the value by ten: the ones place, the tens place, the hundreds place, the thousands place, and so on. The number 3,456 breaks down as 3 thousands, 4 hundreds, 5 tens, and 6 ones.

Understanding place value helps you grasp why we “carry” numbers when adding or “borrow” when subtracting. When you add 47 + 28, you're really adding 4 tens plus 2 tens (making 6 tens) and 7 ones plus 8 ones (making 15 ones, which becomes 1 ten and 5 ones). Place value also works with decimals: in 3.14, the 1 is in the tenths place and the 4 is in the hundredths place.