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Place value
Why a 5 in 305 means something different from a 5 in 350. The position of a digit decides how much it's worth.
Place value blocks
Each column counts something different
147
Hundreds
1
1 × 100 = 100
Tens
4
4 × 10 = 40
Ones
7
7 × 1 = 7
100 + 40 + 7 = 147
Same digits, different value
Compare 305 and 350. They use the exact same three digits, but they aren't the same number. The reason: each column stands for a different group size.
The columns, right to left
- Ones — single units. 1, 2, 3, …
- Tens — bundles of ten. A "3" here means 30.
- Hundreds — bundles of a hundred. A "3" here means 300.
- Thousands — and it keeps going.
The pattern
Every step left, the column is worth ten times more. That's why our system is called base 10.
Try this
Use the buttons above to make the number 207. Notice that the tens column shows zero — the zero is doing real work, holding the place open.
Reading bigger numbers
To read 1,254 you split it: 1 thousand, 2 hundreds, 5 tens, 4 ones. That's "one thousand, two hundred and fifty-four."
Quick check
- What is the value of the 7 in 472?
- Write 800 + 60 + 3 as a single number.
- Which is bigger, 4,099 or 4,100?
Answers: 70, 863, 4,100.