A three-digit number like 247 can be decomposed as 2 hundreds + 4 tens + 7 ones, or 200 + 40 + 7. Understanding this decomposition is essential for addition, subtraction, and developing number sense about magnitude.
Use base-ten blocks (flats for hundreds, rods for tens, units for ones) to represent numbers. Write the expanded form (200 + 40 + 7) alongside the standard form (247). Trade blocks to show equivalent representations.
You already know that our number system is built on place value — that a digit's position tells you what it's worth. You've seen this with two-digit numbers: the 3 in 35 means 30, not 3. Three-digit number decomposition extends that same idea one more place to the left, adding hundreds.
Take the number 247. The digit 2 sits in the hundreds place, so it represents 2 × 100 = 200. The 4 sits in the tens place, so it represents 4 × 10 = 40. The 7 sits in the ones place, so it represents 7 × 1 = 7. Put it all together and you get the expanded form: 200 + 40 + 7. The standard form (247) and the expanded form are just two ways of writing the same number — like saying "two hundred forty-seven" out loud. The value doesn't change, only the notation.
This matters enormously when you add or subtract large numbers. When you add 247 + 135, you're really adding the hundreds together (200 + 100), the tens together (40 + 30), and the ones together (7 + 5). Decomposition is the hidden engine inside the column-addition algorithm you've learned. Understanding it means you're not just following steps — you know *why* the steps work.
Watch out for zeros, which are the trickiest case. The number 305 decomposes as 300 + 0 + 5, or just 300 + 5. The zero in the tens place is a placeholder — it tells you there are no tens — but it's still worth zero, not nothing. Writing the zero is what keeps the 3 in the hundreds position and the 5 in the ones position. If you forgot it and wrote 35, you'd have a completely different number.