Numbers up to 1000 and Place Value: Class 3 Study Guide
Each digit in a number has a place and a value. Knowing them lets you read, compare and order any number.
We write numbers with ten digits, 0 to 9. In a three-digit number, the digit on the right is the ones place, the middle digit is the tens place and the digit on the left is the hundreds place. In 456, the 4 means 4 hundreds (400), the 5 means 5 tens (50) and the 6 means 6 ones (6). So 456 = 400 + 50 + 6. This is called the expanded form.
Ten ones make one ten, ten tens make one hundred, and ten hundreds make one thousand. Understanding this 'groups of ten' idea helps you understand why we carry and borrow when we add and subtract.
Place value chart
A place value chart shows the value of each digit.
| Number | Hundreds (H) | Tens (T) | Ones (O) | Expanded form |
|---|---|---|---|---|
| 238 | 2 | 3 | 8 | 200 + 30 + 8 |
| 705 | 7 | 0 | 5 | 700 + 0 + 5 |
| 999 | 9 | 9 | 9 | 900 + 90 + 9 |
| 1000 | 10 | 0 | 0 | One thousand |
Face value and place value
The face value of a digit is the digit itself. The place value is the digit multiplied by its position. In 564, the face value of 6 is 6 but its place value is 60. The digit 0 has no value of its own, but it keeps other digits in their correct places (as in 705).
Comparing and ordering
To compare, look at the hundreds first. The number with more hundreds is bigger. If hundreds are equal, compare tens, then ones. Use > (greater than), < (less than) or = (equal to). 482 > 428 because the hundreds are the same but 8 tens is more than 2 tens.
Is one number larger?
Compare the tens digits.
Decide which is greater.
Largest and smallest numbers
Take three digits: 3, 7, 5. To make the greatest number, put the biggest digit in the hundreds place: 753. To make the smallest, put the smallest digit first: 357. If one digit is 0, the smallest three-digit number cannot start with 0: using 0, 4, 9 the smallest is 409, not 049. A frequent mistake is to forget this rule.
Check your understanding: model answers
1. 307 = 300 + 0 + 7. 2. 698 is greater because the hundreds are the same, but 9 tens is more than 8 tens. 3. The largest is 962 and the smallest is 269.
✨ Key Takeaways
- A three-digit number has hundreds, tens and ones.
- Expanded form shows each digit's value: 456 = 400 + 50 + 6.
- Compare numbers from the hundreds place first.
- The smallest three-digit number cannot begin with zero.
💬 Questions for Discussion & Reflection
- Write 307 in expanded form.
- Which is greater, 689 or 698? Explain.
- Using the digits 2, 6 and 9, make the largest and the smallest numbers.