Three-digit numbers have hundreds, tens, and ones places. 347 = 3 hundreds + 4 tens + 7 ones = 300 + 40 + 7. Understanding place value is essential for operations and rounding.
Use base-ten blocks (flats, rods, units). Write numbers in expanded form.
Confusing digit with place value; not understanding regrouping; misplacing values.
You already understand that two-digit numbers are made of tens and ones. The number 47 means 4 tens and 7 ones — not 47 separate objects, but a bundled structure. Three-digit numbers extend that same idea by adding one more level: hundreds. Just as 10 ones bundle into 1 ten, 10 tens bundle into 1 hundred. The system keeps going by the same rule at every level.
So the number 347 isn't just "three-four-seven." It means: 3 groups of one hundred, 4 groups of ten, and 7 ones. Expanded form makes this visible: 347 = 300 + 40 + 7. That's a powerful notation because it shows the value each digit actually contributes. The digit 3 in 347 is worth 300 — not 3. Its position (the hundreds place) is what gives it that value. This is the essential idea of a positional number system: the same digit has different values depending on where it sits.
With base-ten blocks, a hundreds flat is a square of 100 small cubes. To show 347, you'd lay out 3 flats, 4 rods, and 7 unit cubes. Notice that 3 flats + 4 rods + 7 units is the same total as 347 loose unit cubes — just organized. This bundling is what makes arithmetic manageable; operating on 3 organized groups of 100 is much easier than counting 300 individual cubes.
Understanding three-digit place value also means recognizing zeros as placeholders. The number 305 has a 0 in the tens place — meaning there are 0 tens, just 3 hundreds and 5 ones. Without that zero, 305 would collapse to 35, an entirely different number. The zero's job is to hold the position so the 3 stays in the hundreds place and the 5 stays in the ones place. This will become critical when you start adding and subtracting multi-digit numbers, where regrouping moves value between these exact positions.