Rounding: Making a number simpler but keeping its value close to what it was
Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, etc.)
Nearest 10: The closest multiple of 10 to a given number
Nearest 100: The closest multiple of 100 to a given number
Estimation: Using rounded numbers to get an approximate answer
- Identify place values: Locate tens and ones digits
- Look at ones digit: Only the ones digit determines rounding direction
- Apply rule: If ones digit ≥ 5, round UP; if ≤ 4, round DOWN
- Change trailing digits: Set all digits to the right of tens to zero
- Identify place values: Locate hundreds, tens, and ones digits
- Look at tens digit: Only the tens digit determines rounding direction
- Apply rule: If tens digit ≥ 5, round UP; if ≤ 4, round DOWN
- Change trailing digits: Set all digits to the right of hundreds to zero
• Ones digit rule (to nearest 10): If ones digit ≥ 5, round up; if ≤ 4, round down
• Tens digit rule (to nearest 100): If tens digit ≥ 5, round up; if ≤ 4, round down
• Halfway cases: When exactly halfway (digit = 5), round up
• Trailing zeros: Digits to the right of the rounding place become zeros
• Ones digit is 7 (≥ 5) → Round UP to 70
• Ones digit is 2 (≤ 4) → Round DOWN to 40
• Ones digit is 5 (= 5) → Round UP to 40
• Ones digit is 6 (≥ 5) → Round UP to 160
• Tens digit is 6 (≥ 5) → Round UP to 600
• Tens digit is 2 (≤ 4) → Round DOWN to 400
• Tens digit is 5 (= 5) → Round UP to 800
• Tens digit is 4 (≤ 4) → Round DOWN to 1,200
| Number | Ones Digit | Direction | Answer |
|---|---|---|---|
| 24 | 4 | Down | 20 |
| 78 | 8 | Up | 80 |
| 155 | 5 | Up | 160 |
| 432 | 2 | Down | 430 |
| 679 | 9 | Up | 680 |
| Number | Tens Digit | Direction | Answer |
|---|---|---|---|
| 347 | 4 | Down | 300 |
| 689 | 8 | Up | 700 |
| 1,250 | 5 | Up | 1,300 |
| 4,523 | 2 | Down | 4,500 |
| 7,845 | 4 | Down | 7,800 |
• Always identify place values first
• Focus on the correct digit
• Remember the "5 and above" rule
• Set trailing digits to zero after rounding
• Check your answer is a multiple of 10 or 100
Ones place: Rightmost digit
Tens place: Second from right
Hundreds place: Third from right
Thousands place: Fourth from right
- Identify the rounding place: Determine if rounding to nearest 10 or 100
- Locate the target digit: Find the digit one place to the right of the rounding place
- Apply the rule: If target digit ≥ 5, round up; if ≤ 4, round down
- Change digits: Keep digits to the left of rounding place, set others to zero
- Verify: Check that your answer makes sense
• Nearest 10 Rule: Look at ones digit, round up if ≥ 5, down if ≤ 4
• Nearest 100 Rule: Look at tens digit, round up if ≥ 5, down if ≤ 4
• Halfway Convention: When target digit = 5, round up
• Trailing Zeros: After rounding, digits to the right become zeros
• Estimation Strategy: Rounding simplifies numbers for easier calculation
Questions & Answers
Question: I'm confused about when to round to the nearest 10 versus the nearest 100. How do I know which one to do?
Answer: The problem will usually tell you which one to do! Look for specific instructions:
- "Round to the nearest 10": Look for the tens place and focus on the ones digit
- "Round to the nearest 100": Look for the hundreds place and focus on the tens digit
Examples:
- Round 247 to the nearest 10 → Focus on ones digit (7) → Answer: 250
- Round 247 to the nearest 100 → Focus on tens digit (4) → Answer: 200
The key is to identify which place value you're rounding to, then look at the digit immediately to its right.
Question: When I round 350 to the nearest 100, it seems like it should stay the same since it ends in 50. Why does it become 400?
Answer: This is a common source of confusion! When rounding to the nearest 100, you only look at the tens digit, not the entire last two digits.
In 350:
- The hundreds digit is 3
- The tens digit is 5
- The ones digit is 0
Since the tens digit is 5 (which equals 5), we round UP to the next hundred: 400.
Remember the rule: when the target digit (tens digit for nearest 100) is 5 or greater, we round up. The ones digit doesn't matter when rounding to the nearest 100.
Question: I sometimes forget to change the digits to the right of the rounding place to zero. Any tips?
Answer: This is a very common mistake! Here are some strategies to help:
- Circle the rounding place: Circle the digit you're rounding to, then cross out everything to the right
- Replace with zeros: After crossing out, write zeros in those positions
- Check your work: Make sure your answer is a multiple of 10 (for nearest 10) or 100 (for nearest 100)
Example: Rounding 473 to nearest 10:
- Focus on tens place (7), ones digit is 3 (≤ 4) → Round down
- Cross out the 3, replace with 0 → 470
- Check: 470 is a multiple of 10 ✓
Practice this process several times until it becomes automatic!