You’ve been using this system since you counted on your fingers. Ten fingers, ten digits — 0 through 9. When you run out, you don’t invent a new symbol. You carry left.

That carrying is the key. The decimal system is a positional system: the value of a digit depends not just on what it is, but where it sits.

In 385:

• 5 is in the ones place → 5 × 1
• 8 is in the tens place → 8 × 10
• 3 is in the hundreds place → 3 × 100

Position = power of 10. Move one step left, multiply by ten.

Decimal = base-10 — ten symbols, positional value, carry at ten.

This feels obvious because it’s invisible — you’ve never had to think about it. But once you do, you can learn any number system. They all follow the same logic, just with a different base.

The Pattern

Ones → Tens → Hundreds → Thousands → …

10⁰ → 10¹ → 10² → 10³ → ...

Every number system is just this pattern with a different base. Decimal uses 10. Soon you’ll meet ones that use 2, 8, and 16.