Place Value
Each digit’s value depends on its position.
Formula
Variables
Example
342 = 3×100 + 4×10 + 2
How it works
In base-10 numbers, a digit’s value depends on how far it is from the rightmost digit. The rightmost position is ones, the next is tens, then hundreds, so each place is a power of 10, which is why the total number is found by adding each digit multiplied by its place value. This works because our number system groups quantities in tens, so every shift left makes the value 10 times larger.
When to use it
Use this when you want to break a number into expanded form, compare digits by place, or understand how large multi-digit numbers are built. It is especially useful in early arithmetic, reading large numbers, and checking calculations.
Worked example, step by step
Find the place value expansion of 5,708. 5,708 = 5×10^3 + 7×10^2 + 0×10^1 + 8×10^0 5,708 = 5×1000 + 7×100 + 0×10 + 8×1 5,708 = 5000 + 700 + 0 + 8 5,708 = 5708
Common mistakes to avoid
- Starting place values at 1 instead of 0 for the ones digit
- Confusing the digit itself with its place value, such as saying 7 always means seventy
- Forgetting that a zero digit still matters because it shows a missing place
Did You Know?
The place-value system with zero, developed in India, is considered one of humanity's greatest inventions — without it, arithmetic would be crippling.
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