Place Value
“A digit's worth comes from where it stands, not just what it is.”
The hook
The same digit 3 can mean three hundred or just three — all because of where it sits.
In plain words
A digit's value depends on which spot (place) it stands in.
The intuition
Reading from the right: ones, tens, hundreds. Every step to the left is worth 10 times more. So 372 is a 3 worth 300, a 7 worth 70, and a 2 worth 2.
How it's built
Each place has a value: ones (1), tens (10), hundreds (100), thousands (1000). Multiply the digit by its place value to get what it really counts.
Example
372 = (3×100) + (7×10) + (2×1) = 300 + 70 + 2. Here the 3 means 300, not 3.
Common mistake
Don't judge a digit by its shape alone. The 5 in 4567 is not 5 but 500, because it sits in the hundreds place.
Where it's used
Counting money, reading big numbers, lining up columns to add or subtract — every number skill rests on place value.
Where it came from
Using 0 to hold an empty place was polished in ancient India and spread worldwide through the Arabic numerals.
Quick check
In 4567, what value does the digit 5 stand for?
- 5
- 50
- 500✓
- 5000
Practice
Write the value that the digit 8 stands for in 806.
Answer: 800
- The 8 sits in the hundreds place.
- 8 × 100 = 800
Takeaway: Multiply the digit by its place to get its real value.
What number is 500 + 40 + 7?
Answer: 547
- Hundreds 5, tens 4, ones 7
- → 547
Takeaway: Snap the place values back together to make one number.
In 2390, what value does the digit 3 stand for?
Answer: 300
- The 3 sits in the hundreds place.
- 3 × 100 = 300
Takeaway: The same 3 means 300 when it sits in the hundreds place.