Place Value Mastery

Mental Math · Axiom Academy

A number is really a sum of its places — and reading those places on sight is what powers every mental-math trick. Say the number 537 and you are really naming three things at once: 5 hundreds, 3 tens, and 7 ones. Each digit's value depends on the place it sits in — its position, not just its face. Each digit is worth its face value times its place The digits change but the idea does not — 365 is 3 hundreds, 6 tens, and 5 ones: 2. Each Place Is Worth Ten Times More Watch a single digit 5 . In the ones place it is worth 5. Slide it one place left and it is worth 50 — ten times as much. Slide it again and it is 500. Every step left multiplies the value by 10 . Because a number is its places, you can add two numbers place by place instead of all at once. Take 34 + 52 : add the tens to the tens, add the ones to the ones, then put the pieces back together. Line up hundreds with hundreds, tens with tens, ones with ones. For 245 + 132 that is 300 + 70 + 7: You can now read any number as its places — and use that skeleton to split, add, and rebuild in your head. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Mental Math course.