Solved Exercises on Rounding Numbers to Nearest 10 and 100 in Grade 4

Master rounding numbers: place value, rules for rounding to nearest 10 and 100, visual number lines, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Rounding to Nearest 10
Exercise 1
Round 47 to the nearest 10.
Show your work using place value and number line.
Definition:

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

Rounding method:
  1. Identify the tens and ones digits
  2. Look at the ones digit (rightmost digit)
  3. If ones digit ≥ 5, round UP to next ten
  4. If ones digit < 5, round DOWN to previous ten
4
Tens
7
Ones
Step 1: Identify place values

In 47: Tens digit = 4, Ones digit = 7

Step 2: Apply rounding rule

Ones digit is 7, which is ≥ 5, so we round UP

Step 3: Find the rounded number

47 is between 40 and 50. Since 7 ≥ 5, we round up to 50

40
45
50
↑
47
47 rounds to 50
Final answer:

47 rounds to 50 because the ones digit (7) is greater than or equal to 5

Applied rules:

• Round UP: When ones digit ≥ 5

• Round DOWN: When ones digit < 5

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

2 Rounding to Nearest 10 (Down)
Exercise 2
Round 83 to the nearest 10.
Show your work using place value and number line.
Definition:

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

8
Tens
3
Ones
Step 1: Identify place values

In 83: Tens digit = 8, Ones digit = 3

Step 2: Apply rounding rule

Ones digit is 3, which is < 5, so we round DOWN

Step 3: Find the rounded number

83 is between 80 and 90. Since 3 < 5, we round down to 80

80
85
90
↑
83
83 rounds to 80
Final answer:

83 rounds to 80 because the ones digit (3) is less than 5

Applied rules:

• Round UP: When ones digit ≥ 5

• Round DOWN: When ones digit < 5

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

3 Rounding to Nearest 100
Exercise 3
Round 367 to the nearest 100.
Show your work using place value and number line.
Definition:

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

3
Hundreds
6
Tens
7
Ones
Step 1: Identify place values

In 367: Hundreds digit = 3, Tens digit = 6, Ones digit = 7

Step 2: Apply rounding rule

Look at the tens digit (6). Since 6 ≥ 5, we round UP

Step 3: Find the rounded number

367 is between 300 and 400. Since tens digit (6) ≥ 5, we round up to 400

300
350
400
↑
367
367 rounds to 400
Final answer:

367 rounds to 400 because the tens digit (6) is greater than or equal to 5

Applied rules:

• Round UP: When tens digit ≥ 5

• Round DOWN: When tens digit < 5

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

Rounding Rules and Methods
\(\text{Round to nearest 10: Look at ones digit}\)
Rounding to Nearest 10
Rule 1
Ones ≥ 5 → Round UP
Round to higher multiple
Rule 2
Ones < 5 → Round DOWN
Round to lower multiple
Rule 3
Tens ≥ 5 → Round UP
For nearest 100
📊
Place Value
Focus on specific digits for each rounding level
🔄
Round Up/Down
Based on comparison with 5
🎯
Closest Multiple
Find nearest 10 or 100
Key Concept: Rounding makes numbers simpler while keeping their value close to the original.
Practical Use: Estimation, budgeting, measuring, and simplifying calculations.
Tip 1: For nearest 10, focus only on the ones digit.
Tip 2: For nearest 100, focus only on the tens digit.
Tip 3: Remember: 5 rounds UP, not down!
Solution: Exercises 4 to 5
4 Rounding to Nearest 100 (Down)
Exercise 4
Round 524 to the nearest 100.
Show your work using place value and number line.
Definition:

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

5
Hundreds
2
Tens
4
Ones
Step 1: Identify place values

In 524: Hundreds digit = 5, Tens digit = 2, Ones digit = 4

Step 2: Apply rounding rule

Look at the tens digit (2). Since 2 < 5, we round DOWN

Step 3: Find the rounded number

524 is between 500 and 600. Since tens digit (2) < 5, we round down to 500

500
550
600
↑
524
524 rounds to 500
Final answer:

524 rounds to 500 because the tens digit (2) is less than 5

Applied rules:

• Round UP: When tens digit ≥ 5

• Round DOWN: When tens digit < 5

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

5 Mixed Practice
Exercise 5
Round 847 to the nearest 10 and nearest 100.
Show both answers with step-by-step work.
Definition:

Rounding to nearest 10 and 100: Applying different rounding rules to the same number

8
Hundreds
4
Tens
7
Ones
Step 1: Round to nearest 10

Look at ones digit (7). Since 7 ≥ 5, round UP to 850

Step 2: Round to nearest 100

Look at tens digit (4). Since 4 < 5, round DOWN to 800

Step 3: Verify with number lines

Nearest 10: 847 is between 840 and 850 → closer to 850

Nearest 100: 847 is between 800 and 900 → closer to 800

840
845
850
↑
847
800
850
900
↑
847
847 → 850 (nearest 10)
847 → 800 (nearest 100)
Final answers:

Nearest 10: 847 → 850

Nearest 100: 847 → 800

Applied rules:

• Nearest 10: Look at ones digit (7 ≥ 5 → round UP)

• Nearest 100: Look at tens digit (4 < 5 → round DOWN)

• Same number: Different rounding levels give different results

Rounding Laws, Methods, Rules, and Key Concepts
\(\text{Ones digit} \geq 5 \Rightarrow \text{Round UP}\)
Rounding Rule
Key definitions:

Rounding: Making a number simpler while keeping its value close to the original

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

Multiple of 10: Numbers like 10, 20, 30, 40, etc.

Multiple of 100: Numbers like 100, 200, 300, 400, etc.

Complete methodology:
  1. Identify place values: Know which digit to focus on
  2. For nearest 10: Look at the ones digit
  3. For nearest 100: Look at the tens digit
  4. Compare with 5: Apply rounding rule
  5. Round accordingly: UP if ≥ 5, DOWN if < 5
Tip 1: Use number lines to visualize the rounding process.
Tip 2: Remember that 5 always rounds UP, never down.
Tip 3: Practice with different place values to master the concept.
Tip 4: Check your answer by seeing if the rounded number is reasonable.
Common errors: Looking at wrong digit, forgetting 5 rounds up, mixing up place values.
Real-world use: Estimating costs, measuring distances, calculating approximate totals.
Rounding rules to remember:

• Round to nearest 10: Look at ones digit

• Round to nearest 100: Look at tens digit

• Round UP: When target digit ≥ 5

• Round DOWN: When target digit < 5

• Keep higher places: Don't change digits in higher place values

Real-World Rounding Applications
Practical Examples
Rounding is used in many real-life situations:
• Shopping: Estimating total costs
• Travel: Approximating distances
• Cooking: Measuring ingredients
• Sports: Calculating scores
🛒
Shopping
$27 → $30 for quick estimates
🚗
Travel
147 miles → 150 miles for planning
🍳
Cooking
Recipe measurements

Why round? Makes calculations easier and gives approximate answers that are good enough for many purposes.

Questions & Answers

Question: I don't understand why we round UP when the digit is 5. Why isn't 5 in the middle just stay the same?

Answer: Great question! The reason 5 always rounds UP is to maintain consistency in our rounding system. Think of it this way:

  • Numbers 0, 1, 2, 3, 4 are clearly closer to the lower multiple
  • Numbers 6, 7, 8, 9 are clearly closer to the higher multiple
  • Number 5 is exactly in the middle, so we made a rule that it rounds UP

This ensures that when we round many numbers, we don't consistently round down, which would make our estimates too low. By always rounding 5 up, we balance out the rounding over many calculations.

Example: 35 rounds to 40 (not staying at 35), and 45 rounds to 50.

Question: My child gets confused about which digit to look at. How can I help them remember when rounding to nearest 10 vs nearest 100?

Answer: Here's a helpful memory trick for your child:

  • Nearest 10: Count the "ZEROS" in 10 (one zero), so look at the digit ONE place to the right of where the zero would be (the ones place)
  • Nearest 100: Count the "ZEROS" in 100 (two zeros), so look at the digit TWO places to the right of where the zeros would be (the tens place)

Another way to remember: When rounding to 10, we're looking for which "ten" the number is closest to (20, 30, 40, etc.). When rounding to 100, we're looking for which "hundred" it's closest to (200, 300, 400, etc.).

Practice with place value charts to reinforce which digit corresponds to which place!

Question: Why do we need to learn rounding? When will I ever use this in real life?

Answer: Rounding is incredibly useful in daily life! Here are some examples:

  • Shopping: If something costs $27, you might round to $30 to estimate if you have enough money
  • Time: Saying "about 30 minutes" instead of exactly 28 minutes
  • Distance: Saying a city is "about 100 miles away" instead of 97 miles
  • Budgeting: Rounding prices helps you quickly calculate approximate totals

Rounding helps us make quick decisions and estimates without needing exact calculations every time. It's also important for checking if your exact answers make sense!

Think of rounding as giving "good enough" answers that are easier to work with!