Rounding Whole Numbers to the Nearest 10 or 100 - Complete Guide

Master rounding whole numbers to the nearest 10 or 100 with these 5 detailed exercises and visual explanations.

Solution: Exercises 1 to 3
1 Rounding to the nearest 10
Exercise 1
Round 78 to the nearest 10.
Definition:

Rounding to the nearest 10: Finding the closest multiple of 10 to a given number.

Rounding method:
  1. Look at the digit in the ones place (rightmost digit)
  2. If the ones digit is 0, 1, 2, 3, or 4 → round down
  3. If the ones digit is 5, 6, 7, 8, or 9 → round up
  4. Change the ones digit to 0 and keep other digits the same
Number
78
Ones digit
8
Result
80
Step 1: Identify the ones digit

In 78, the ones digit is 8.

Step 2: Apply the rounding rule

Since 8 ≥ 5, we round up to the next multiple of 10.

Step 3: Change the ones digit to 0

Keep the tens digit (7) and change the ones digit to 0, then add 1 to tens: 70 + 10 = 80.

60
65
70
75
80
85
90
78
80
78 rounded to the nearest 10 is 80
Final answer:

78 rounded to the nearest 10 is 80

Applied rules:

• Rounding Rule: If ones digit ≥ 5, round up; if ones digit ≤ 4, round down

• Place Value: Focus on the ones place for rounding to nearest 10

• Multiples of 10: Numbers ending in 0 (10, 20, 30, 40, etc.)

2 Rounding to the nearest 10
Exercise 2
Round 234 to the nearest 10.
Definition:

Rounding to the nearest 10: Finding the closest multiple of 10 to a given number.

Number
234
Ones digit
4
Result
230
Step 1: Identify the ones digit

In 234, the ones digit is 4.

Step 2: Apply the rounding rule

Since 4 ≤ 4, we round down to the previous multiple of 10.

Step 3: Change the ones digit to 0

Keep the tens and hundreds digits (23) and change the ones digit to 0: 230.

220
225
230
235
240
245
250
234
230
234 rounded to the nearest 10 is 230
Final answer:

234 rounded to the nearest 10 is 230

Applied rules:

• Rounding Rule: If ones digit ≥ 5, round up; if ones digit ≤ 4, round down

• Place Value: Focus on the ones place for rounding to nearest 10

• Multiples of 10: Numbers ending in 0 (10, 20, 30, 40, etc.)

3 Rounding to the nearest 100
Exercise 3
Round 467 to the nearest 100.
Definition:

Rounding to the nearest 100: Finding the closest multiple of 100 to a given number.

Number
467
Tens digit
6
Result
500
Step 1: Identify the tens digit

In 467, the tens digit is 6 (the digit in the tens place).

Step 2: Apply the rounding rule

Since 6 ≥ 5, we round up to the next multiple of 100.

Step 3: Change the tens and ones digits to 0

Keep the hundreds digit (4) and change the tens and ones digits to 0, then add 1 to hundreds: 400 + 100 = 500.

300
350
400
450
500
550
467
500
467 rounded to the nearest 100 is 500
Final answer:

467 rounded to the nearest 100 is 500

Applied rules:

• Rounding Rule: If tens digit ≥ 5, round up; if tens digit ≤ 4, round down

• Place Value: Focus on the tens place for rounding to nearest 100

• Multiples of 100: Numbers ending in 00 (100, 200, 300, 400, etc.)

Rules and methods, laws,...
Ones digit ≥ 5 → Round UP
Ones digit ≤ 4 → Round DOWN
Rounding to Nearest 10
Tens digit ≥ 5 → Round UP
Tens digit ≤ 4 → Round DOWN
Rounding to Nearest 100
Rule 1
Round to nearest 10
Focus on ones digit
Rule 2
Round to nearest 100
Focus on tens digit
Rule 3
Round UP
Digit ≥ 5
Key definitions:

Rounding: Making a number simpler but keeping its value close to what it was

Nearest 10: The multiple of 10 that is closest to the original number

Nearest 100: The multiple of 100 that is closest to the original number

Complete methodology:
  1. Identify the place value: Determine if rounding to nearest 10 or 100
  2. Locate the target digit: For nearest 10, look at ones digit; for nearest 100, look at tens digit
  3. Apply the rule: If target digit ≥ 5, round up; if target digit ≤ 4, round down
  4. Adjust the number: Change appropriate digits to 0 and adjust higher place values if needed
Tip 1: Think of rounding as finding the closest "friend" that ends in 0 (for 10) or 00 (for 100).
Tip 2: Use a number line to visualize which multiple of 10 or 100 is closer.
Tip 3: Remember: 5 is the "tie-breaker" - when the digit is exactly 5, we round up.
Tip 4: When rounding up, add 1 to the higher place value.
Common errors: Looking at wrong place value, forgetting to change lower digits to 0, misapplying the 5 rule.
Memory aid: "5 or more, raise the score; 4 or less, let it rest."
Key rules to remember:

• To nearest 10: Look at ones digit, round up if ≥ 5, down if ≤ 4

• To nearest 100: Look at tens digit, round up if ≥ 5, down if ≤ 4

• Change digits: When rounding, make lower place values 0

• Add 1: When rounding up, increase the target place value by 1

Solution: Exercises 4 to 5
4 Rounding to the nearest 100
Exercise 4
Round 823 to the nearest 100.
Definition:

Rounding to the nearest 100: Finding the closest multiple of 100 to a given number.

Number
823
Tens digit
2
Result
800
Step 1: Identify the tens digit

In 823, the tens digit is 2 (the digit in the tens place).

Step 2: Apply the rounding rule

Since 2 ≤ 4, we round down to the previous multiple of 100.

Step 3: Change the tens and ones digits to 0

Keep the hundreds digit (8) and change the tens and ones digits to 0: 800.

700
750
800
850
900
950
823
800
823 rounded to the nearest 100 is 800
Final answer:

823 rounded to the nearest 100 is 800

Applied rules:

• Rounding Rule: If tens digit ≥ 5, round up; if tens digit ≤ 4, round down

• Place Value: Focus on the tens place for rounding to nearest 100

• Multiples of 100: Numbers ending in 00 (100, 200, 300, 400, etc.)

5 Mixed rounding
Exercise 5
Round 547 to the nearest 10 and to the nearest 100.
Definition:

Mixed rounding: Applying different rounding rules to the same number.

Number
547
To nearest 10
550
To nearest 100
500
Step 1: Round to nearest 10

Look at ones digit: 7. Since 7 ≥ 5, round up to 550.

Step 2: Round to nearest 100

Look at tens digit: 4. Since 4 ≤ 4, round down to 500.

Step 3: Compare results

547 → 550 (nearest 10) and 547 → 500 (nearest 100)

🎯
Nearest 10: Look at ones digit (7)
➡️
Round up since 7 ≥ 5
✅
Result: 550
🎯
Nearest 100: Look at tens digit (4)
➡️
Round down since 4 ≤ 4
✅
Result: 500
547 rounded to nearest 10 is 550
547 rounded to nearest 100 is 500
Final answer:

547 rounded to nearest 10 is 550
547 rounded to nearest 100 is 500

Applied rules:

• For nearest 10: Look at ones digit (7), since 7 ≥ 5, round up to 550

• For nearest 100: Look at tens digit (4), since 4 ≤ 4, round down to 500

• Different results: Same number can have different rounded values depending on place value

Rounding Rules, Methods, and Practice Guide
"5 or more, raise the score"
"4 or less, let it rest"
Rounding Memory Aid
Key definitions:

Rounding: Replacing a number with another number that tells about how many or how much

Estimation: Using rounded numbers to find an answer that is close enough to the exact answer

Place Value: The value of each digit based on its position in the number

Complete methodology:
  1. Identify rounding target: Determine if rounding to nearest 10, 100, or other place
  2. Find the target digit: For 10s, look at ones; for 100s, look at tens; for 1000s, look at hundreds
  3. Apply rounding rule: If target digit ≥ 5, round up; if target digit ≤ 4, round down
  4. Make changes: Change all digits to the right of the target place to 0
  5. Adjust if needed: If rounding up, increase the target place value by 1
Tip 1: When rounding 9s, you might need to regroup (e.g., 299 rounds to 300 when rounding to nearest 100).
Tip 2: Use number lines to visualize where the number falls between multiples.
Tip 3: Always underline or circle the target digit to avoid confusion.
Tip 4: Check your work by ensuring the rounded number makes sense compared to the original.
Common errors: Looking at wrong place value, forgetting to change digits to 0, not adjusting when rounding up past 9.
Real-world use: Estimating costs, distances, populations, and other quantities for easier calculations.
Essential rounding rules:

• Nearest 10: Look at ones digit, round up if ≥ 5, down if ≤ 4

• Nearest 100: Look at tens digit, round up if ≥ 5, down if ≤ 4

• Nearest 1000: Look at hundreds digit, round up if ≥ 5, down if ≤ 4

• Change digits: Make all digits to the right of target place equal to 0

• Regrouping: When rounding up causes a 9 to become 10, carry over to the next place value

Examples:
347 → 350 (nearest 10)
347 → 300 (nearest 100)
752 → 750 (nearest 10)
752 → 800 (nearest 100)
Practice Examples

Questions & Answers

Question: I don't understand why we round 5 up instead of down. Why is that the rule?

Answer: Great question! We round 5 up because it's exactly in the middle between two multiples, so we need a consistent rule. Here's why:

  • When we have a number like 35, it's equally close to 30 and 40
  • Instead of having a separate rule for 5, mathematicians decided to always round up when the digit is 5 or more
  • This creates a consistent pattern: 0,1,2,3,4 round down; 5,6,7,8,9 round up
  • It also helps avoid bias in statistics - if we always rounded 5 down, we'd consistently underestimate

Think of it as a tie-breaker: when there's a tie, we break it by going up!

Question: My child keeps getting confused about which digit to look at when rounding. Any tips to help them remember?

Answer: Here are some helpful strategies to teach your child:

  • Count backwards: For rounding to nearest 10, count back 1 place (ones digit); for nearest 100, count back 2 places (tens digit)
  • Circle the digit: Have your child circle the digit they need to look at before rounding
  • Memory phrase: "Look at the one behind the one you want" - if rounding to 10s, look at the ones place
  • Visual aids: Draw arrows pointing to the digit that matters for each rounding situation

Practice with the same number rounded to different place values to reinforce the concept!

Question: What happens when I have to round 99 to the nearest 10? The 9 has to go up to 10!

Answer: Excellent observation! When rounding 99 to the nearest 10, here's what happens:

  • Look at the ones digit: 9
  • Since 9 ≥ 5, we round up
  • The ones digit becomes 0, and we add 1 to the tens place
  • The tens place is 9, so adding 1 makes it 10
  • This means 99 rounds up to 100

This is called regrouping - when rounding causes a digit to become 10, it moves to the next place value. It's perfectly normal!