Building Numbers

Pre-Algebra · Axiom Academy

A digit's value depends on WHERE it sits. See how every whole number is built, one place at a time. The same digit, different jobs Look at the number 3,425. There are two 4-ish-looking digits doing very different work: the 4 is worth four hundred , while the 2 next to it is worth only twenty . A digit's value isn't just the digit — it's the digit times the value of the spot it lands in. Watch a number get built that way, then build your own. Watch the marker sweep across the four columns. As it reaches each place, that digit drops in and its piece of the number — digit × place value — gets added to a running total that climbs to the whole number, 3,425. The number is just the sum of its place-value pieces: 3,000 + 400 + 20 + 5. Set a digit (0–9) in each column. The chart fills the spots, the breakdown shows what each digit is worth, and the columns add up to your number. Try putting the same digit in two different columns and watch its value change. Every whole number is built this way — a digit in each place, each place worth ten times the one to its right. Slide one digit and watch it grow Here's a single digit, 4. Drag it left across the columns. Nothing about the digit changes — but each step to the left lands it in a place worth ten times as much, so its value multiplies by 10: 4, then 40, then 400, then 4,000. That ×10 jump from one place to the next is the secret behind our whole number system.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.