Number sense
Understanding Place Value
How a digit’s position changes what it means
TRY IT FIRST
Make the idea move
Change the controls and watch what happens. There’s no score—just explore.
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The idea in one sentence
A digit’s place tells you its value: in 352, the 3 means 3 hundreds, not just 3.
Build the number
Think of a number as boxes for different-sized bundles:
| Hundreds | Tens | Ones |
|---|---|---|
| 3 | 5 | 2 |
So 352 is the same as:
\[300 + 50 + 2\]If you have blocks, use a small cube for 1, a stick of ten cubes for 10, and a flat square of one hundred cubes for 100.
What zero is doing
Zero holds a place open. In 407, there are 4 hundreds, no tens, and 7 ones. Without the zero, 47 would be a completely different number.
A quick way to compare numbers
Start at the biggest place and move right. To compare 352 and 329:
- Both have 3 hundreds.
- Compare the tens: 5 tens is more than 2 tens.
- Stop there. That proves $352 > 329$.
Common mix-ups
- Reading 205 as “twenty-five.” Say each place: 2 hundreds, 0 tens, 5 ones.
- Thinking the 6 in 64 and 604 has the same value. It means 60 in 64 and 600 in 604.
- Comparing only the last digit. The biggest place matters first.
Check yourself
What number has 7 hundreds, 3 tens, and 9 ones? Write it in standard form and expanded form.
Answer: 739, which is $700 + 30 + 9$.
ANOTHER WAY TO SEE IT