Rounding and Adding and Subtracting Within 1,000: Grade 3 Study Guide
Estimating with rounded numbers tells you what to expect. Exact work then confirms it.
Rounding replaces a number with a nearby, easier number. It is useful when you only need to know roughly how many, such as when you check whether you have enough money. Rounding also gives a quick check on exact answers: if your exact sum is far from your estimate, look again.
In Grade 3, you round to the nearest 10 and 100, and you add and subtract numbers within 1,000 using place value and the properties of operations.
How to round
Find the digit in the place you are rounding to, then look at the digit to its right. If it is 5 or more, round up. If it is 4 or less, keep the digit the same. Every digit to the right becomes zero.
Rounding examples
Remember that 5 rounds up.
| Number | To nearest 10 | To nearest 100 |
|---|---|---|
| 347 | 350 | 300 |
| 652 | 650 | 700 |
| 905 | 910 | 900 |
| 449 | 450 | 400 |
Adding and subtracting with regrouping
Line up the digits by place value. Start at the ones. If a column adds to 10 or more, regroup (carry) 10 ones as 1 ten. In subtraction, if the top digit is too small, regroup 1 ten as 10 ones.
468 + 275: round to 470 + 280 = 750.
8 + 5 = 13. Write 3, regroup 1 ten.
6 + 7 + 1 = 14 tens: write 4, regroup 1 hundred. 4 + 2 + 1 = 7 hundreds.
The answer 743 is close to the estimate of 750, so it is reasonable.
Worked examples
Example 1. Round 748 to the nearest hundred. The tens digit is 4, so keep the 7: the answer is 700.
Example 2. 365 + 278. Ones: 5 + 8 = 13, write 3, regroup 1. Tens: 6 + 7 + 1 = 14, write 4, regroup 1. Hundreds: 3 + 2 + 1 = 6. The sum is 643. The estimate 370 + 280 = 650 is close.
Example 3. 731 − 468. Ones: 1 is less than 8, so regroup a ten: 11 − 8 = 3. Tens: 2 − 6 needs a regroup: 12 − 6 = 6. Hundreds: 6 − 4 = 2. The answer is 263; check 263 + 468 = 731.
Common mistakes
Students often forget that rounding up from 9 changes the digit to the left (396 rounds to 400 for the nearest hundred). Others subtract the smaller digit from the larger in every column, which gives wrong answers when the top digit is smaller. Always regroup instead. Also, write your digits in tidy columns; most addition errors come from digits that are not lined up.
Check your understanding: model answers
1. 586 rounds to 590 (nearest 10) and 600 (nearest 100). 2. Estimate 640 + 190 = 830. Exactly: 637 + 189 = 826. 3. 804 − 357 = 447. Check: 447 + 357 = 804.
✨ Key Takeaways
- Round up when the next digit is 5 or more; keep the digit when it is 4 or less.
- Estimate first so you can tell whether an exact answer makes sense.
- Line up digits by place value before adding or subtracting.
- Regroup 10 of one place as 1 of the next place when needed.
💬 Questions for Discussion & Reflection
- Round 586 to the nearest 10 and to the nearest 100.
- Estimate and then find 637 + 189.
- Find 804 − 357 and check using addition.