Place Value to 10 000 and Rounding: Year 3 Study Guide
Where a digit sits decides what it is worth. Understanding place value is the key to every number skill that follows.
In our number system there are only ten digits, 0 to 9, but we can write any number by changing where the digits sit. In 4 372 the 4 is worth 4 thousands (4 000), the 3 is worth 3 hundreds (300), the 7 is worth 7 tens (70) and the 2 is worth 2 ones. Zero is a place holder: in 4 072 it shows that there are no hundreds.
In Year 3 you work with numbers up to 10 000. Australian writing leaves a small space instead of a comma in numbers of five digits or more (10 000), and many people also use a space for four-digit numbers (4 372).
Partitioning
Partitioning means splitting a number into parts by place value. 5 806 = 5 000 + 800 + 0 + 6. You can also partition flexibly: 5 806 = 58 hundreds + 6, or 5 000 + 806. Flexible thinking makes mental addition and subtraction much easier.
| Number | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 4 372 | 4 | 3 | 7 | 2 |
| 6 080 | 6 | 0 | 8 | 0 |
| 9 999 | 9 | 9 | 9 | 9 |
| 10 000 | 10 | 0 | 0 | 0 |
Comparing and ordering
Compare from the left. The number with more thousands is larger. If the thousands match, compare the hundreds, and so on. 6 482 is greater than 6 428 because the hundreds match (4), but 8 tens is more than 2 tens. Use the symbols > (greater than), < (less than) and = (equal to): 6 482 > 6 428.
Rounding
Rounding gives an easier number that is close. To round 3 746 to the nearest hundred, look at the tens digit (4). Since it is less than 5, the hundreds stay the same: 3 700. To round 3 768, the tens digit is 6, so the hundreds go up: 3 800. A digit of 5 rounds up. Rounding to estimate helps you check the size of an answer.
Nearest ten, hundred or thousand.
Is the digit 5 or more?
Up if 5 or more; keep if 4 or less.
3 746 to the nearest hundred is 3 700.
Worked examples and common mistakes
Order from smallest: 5 031, 5 301, 5 013, 5 103. Compare hundreds first: 5 013, 5 031, 5 103, 5 301. Write in words: 7 205 is seven thousand, two hundred and five. A frequent mistake is writing 'thousand and sixty' as 1 060 when the number is 1 060 only if there are zero hundreds; always say each place value in order. Another is thinking that a number with more digits is always bigger; this is true only when there are no leading zeros.
Check your understanding: model answers
1. 7 908 = 7 000 + 900 + 8, and also 79 hundreds + 8. 2. 4 190 is greater: both have 4 thousands and 1 hundred, but 9 tens is more than 0 tens. 3. 2 649 rounds to 2 650 (nearest ten) and 2 600 (nearest hundred).
✨ Key Takeaways
- The value of a digit depends on its place.
- Zero holds a place so other digits keep their value.
- Compare numbers starting from the largest place.
- Round by looking at the digit to the right of the place you are rounding to.
💬 Questions for Discussion & Reflection
- Partition 7 908 in two different ways.
- Which is greater, 4 109 or 4 190? Explain how you know.
- Round 2 649 to the nearest ten and nearest hundred.