MISSION · Number sense
Understanding Place Value
How a digit’s position changes what it means
LEVEL 1 · EXPLORE
Make the idea move
Change the controls and watch what happens. Follow your curiosity and see what you notice.
Loading the activity…
LEVEL 2 · LEARN
Unlock the explanation
Open the chapters in any order. Try the examples as you go.
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 \(700 + 30 + 9\).
LEVEL 3 · REFLECT
Add this quest to your trail
When you feel ready, mark this idea as explored. You can always come back and try it again.
EXPLORER STRATEGIES