What you need to know
Every digit in a number has a place, and the place tells you what the digit is worth. In the number 3475, the 3 is not worth three — it is worth three thousand, because it sits in the thousands place. Reading from the right, the places are ones, tens, hundreds and thousands. Each place is worth ten times the place to its right.
| Thousands | Hundreds | Tens | Ones |
|---|
| 3 | 4 | 7 | 5 |
Expanded form
- Write 3475 in expanded form.
- 3 is in the thousands place, so it is worth 3000.
- 4 is in the hundreds place, so it is worth 400.
- 7 is in the tens place, so it is worth 70.
- 5 is in the ones place, so it is worth 5.
- 3475 = 3000 + 400 + 70 + 5.
The value of a digit
- What is the value of the 8 in 2816?
- Count the places from the right: 6 ones, 1 ten, 8 hundreds, 2 thousands.
- The 8 is in the hundreds place, so its value is 800.
Common mistake: leaving out a zero. In 4057 the 0 is a placeholder that shows there are no hundreds. If you drop it and write 457, the number becomes a completely different size.
Comparing and ordering. To compare two numbers with the same number of digits, start at the left and compare one place at a time. The first place where the digits are different tells you which number is bigger. If one number has more digits than the other, it is bigger.
Which is larger: 5241 or 5198?
- Thousands: both have 5, so move on.
- Hundreds: 2 is bigger than 1.
- So 5241 is larger. You do not need to look at the tens or ones.
Rounding
Rounding gives a number that is close to the real one but easier to work with. To round to the nearest 10, look at the ones digit: 5 or more rounds up, 4 or less rounds down. To round to the nearest 100, look at the tens digit in the same way.
Round 368 to the nearest 10 and the nearest 100
- Nearest 10: the ones digit is 8, which is 5 or more, so round up. 368 → 370.
- Nearest 100: the tens digit is 6, which is 5 or more, so round up. 368 → 400.
Check yourself
- What is the value of the 7 in 4712?
- Write 6093 in expanded form.
- Which is larger: 3819 or 3891?
- Round 2746 to the nearest 100.
- Write 5000 + 300 + 2 as a number.
- What number is 10 more than 4995?
Answers: 1. 700 2. 6000 + 90 + 3 3. 3891 4. 2700 5. 5302 6. 5005