Solved Exercises on Rounding Numbers to Nearest 100 in Grade 4

Master rounding numbers to nearest 100: place value, tens digit rule, estimation, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic rounding
Exercise 1
Round 467 to the nearest 100
Definition:

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

Rounding method:
  1. Identify the hundreds digit and the tens digit
  2. Look at the tens digit only
  3. If tens digit ≥ 5, round UP to next hundred
  4. If tens digit ≤ 4, round DOWN to previous hundred
Thousands
-
Hundreds
4
Tens
6
Ones
7
400
467
500
Step 1: Identify the place values

In 467, the hundreds digit is 4, the tens digit is 6, and the ones digit is 7

Step 2: Look at the tens digit

The tens digit is 6, which is greater than 5

Step 3: Apply the rounding rule

Since 6 ≥ 5, we round UP to the next hundred: 500

467 rounded to the nearest 100 is 500
Final answer:

467 → 500

Applied rules:

• Tens digit rule: If tens digit ≥ 5, round up; if ≤ 4, round down

• Place value: Only the tens digit determines rounding direction

• Nearest hundred: Find the closest multiple of 100

2 Rounding down
Exercise 2
Round 823 to the nearest 100
Definition:

Rounding down: When the tens digit is less than 5, we round to the lower hundred

Thousands
-
Hundreds
8
Tens
2
Ones
3
800
823
900
Step 1: Identify the place values

In 823, the hundreds digit is 8, the tens digit is 2, and the ones digit is 3

Step 2: Look at the tens digit

The tens digit is 2, which is less than 5

Step 3: Apply the rounding rule

Since 2 ≤ 4, we round DOWN to the previous hundred: 800

823 rounded to the nearest 100 is 800
Final answer:

823 → 800

Applied rules:

• Tens digit rule: If tens digit ≥ 5, round up; if ≤ 4, round down

• Rounding down: When tens digit is 0, 1, 2, 3, or 4

• Nearest hundred: Find the closest multiple of 100

3 Exact halfway case
Exercise 3
Round 550 to the nearest 100
Definition:

Halfway case: When a number is exactly halfway between two hundreds (tens digit is 5)

Thousands
-
Hundreds
5
Tens
5
Ones
0
500
550
600
Step 1: Identify the place values

In 550, the hundreds digit is 5, the tens digit is 5, and the ones digit is 0

Step 2: Look at the tens digit

The tens digit is 5, which is equal to 5 (the halfway point)

Step 3: Apply the rounding rule for halfway cases

When tens digit is exactly 5, we round UP to the next hundred: 600

550 rounded to the nearest 100 is 600
Final answer:

550 → 600

Applied rules:

• Halfway rule: When tens digit is exactly 5, round up

• Consistency: Always round up when at the halfway point

• Standard convention: This prevents bias in statistical calculations

Rules and methods, laws,...
Tens Digit Rule
Rounding to Nearest 100
Rule 1
If tens digit ≥ 5
Round UP to next hundred
Rule 2
If tens digit ≤ 4
Round DOWN to previous hundred
Rule 3
If tens digit = 5
Round UP to next hundred
Key definitions:

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

Nearest 100: The closest multiple of 100 to a given number

Complete methodology:
  1. Identify place values: Locate hundreds, tens, and ones digits
  2. Focus on tens digit: Only the tens digit determines rounding direction
  3. Apply rule: Round up if tens digit ≥ 5, round down if ≤ 4
  4. Change trailing digits: Set all digits to the right of hundreds to zero
Tip 1: Only look at the tens digit when rounding to nearest 100.
Tip 2: Remember: 5 and above, let it fly (round up)!
Tip 3: When exactly halfway (tens digit = 5), always round up.
Tip 4: Change all digits to the right of hundreds place to zeros.
Common errors: Looking at the ones digit, forgetting to change trailing digits to zero, misidentifying place values.
Key memorization: Tens digit rule, 5 rounds up, change digits to right of hundreds to zero.
Essential formulas and rules:

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

• Halfway Case: When tens digit = 5, round up

• Place Value Focus: Hundreds digit stays, tens and ones determine direction

• Trailing Zeros: Digits to the right of hundreds become zeros

Solution: Exercises 4 to 5
4 Large number rounding
Exercise 4
Round 1,278 to the nearest 100
Definition:

Rounding large numbers: Same rules apply regardless of number size

Thousands
1
Hundreds
2
Tens
7
Ones
8
1,200
1,278
1,300
Step 1: Identify the place values

In 1,278, the thousands digit is 1, the hundreds digit is 2, the tens digit is 7, and the ones digit is 8

Step 2: Look at the tens digit

The tens digit is 7, which is greater than 5

Step 3: Apply the rounding rule

Since 7 ≥ 5, we round UP to the next hundred: 1,300

Step 4: Set trailing digits to zero

We keep the thousands and hundreds digits (1,3), then set tens and ones to zero

1,278 rounded to the nearest 100 is 1,300
Final answer:

1,278 → 1,300

Applied rules:

• Same rule applies: Tens digit still determines direction

• Large numbers: Ignore digits beyond the rounding place

• Trailing zeros: Change digits to the right of hundreds to zero

5 Word problem application
Exercise 5
A school has 482 students. About how many students are there when rounded to the nearest 100?
Definition:

Estimation: Using rounding to get an approximate answer that's easier to work with

Hundreds
4
Tens
8
Ones
2
400
482
500
Step 1: Identify the place values

In 482, the hundreds digit is 4, the tens digit is 8, and the ones digit is 2

Step 2: Look at the tens digit

The tens digit is 8, which is greater than 5

Step 3: Apply the rounding rule

Since 8 ≥ 5, we round UP to the next hundred: 500

Step 4: Interpret the result

About 500 students is a good estimate for 482 students

About 500 students
Final answer:

There are about 500 students in the school

Applied rules:

• Real-world application: Rounding helps make numbers easier to understand

• Estimation: Provides a reasonable approximation

• Context matters: "About" indicates estimation is appropriate

Comprehensive Guide to Rounding Numbers to Nearest 100
Rounding Rules
To Nearest 100
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 a number (ones, tens, hundreds, etc.)

Nearest 100: The closest multiple of 100 to a given number

Estimation: Using rounded numbers to get an approximate answer

Complete methodology:
  1. Identify place values: Locate the hundreds, tens, and ones digits
  2. Focus on tens digit: Only the tens digit determines the rounding direction
  3. Apply the rule: If tens digit ≥ 5, round up; if ≤ 4, round down
  4. Change trailing digits: Set all digits to the right of hundreds place to zero
  5. Verify result: Check that your rounded number makes sense
Memory trick: "5 and above, let it fly" - round up when tens digit is 5 or more.
Focus only on tens: The ones digit doesn't affect rounding to nearest 100.
Halfway rule: When exactly halfway (tens digit = 5), always round up.
Change trailing digits: After rounding, set tens and ones to zero.
Use number lines: Visualize where the number falls between hundreds.
Check reasonableness: Your rounded number should be close to the original.
Common errors: Looking at the ones digit instead of tens, forgetting to change trailing digits to zero, misidentifying place values, rounding the wrong way for halfway cases.
Practical applications: Estimating costs, population figures, distances, inventory counts, and making quick mental calculations.
Real-world contexts: School enrollment, store inventory, distance measurements, budget planning, and statistical reporting.
Essential formulas and rules:

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

• Halfway Case: When tens digit = 5, round up (standard convention)

• Place Value Focus: Only the tens digit determines the rounding direction

• Trailing Zeros: After rounding, digits to the right of hundreds become zeros

• Nearest Multiple: Find the closest multiple of 100

• Estimation Strategy: Rounding simplifies numbers for easier calculation

Questions & Answers

Question: I don't understand why we only look at the tens digit when rounding to the nearest 100. Why don't we consider the ones digit too?

Answer: Great question! When rounding to the nearest 100, we're deciding whether a number is closer to the lower hundred or the higher hundred. Let me explain with an example:

Take the number 467. We need to decide if it's closer to 400 or 500.

  • The hundreds digit (4) tells us we're somewhere between 400 and 500
  • The tens digit (6) tells us how far along we are between 400 and 500
  • The ones digit (7) is just a small adjustment within the tens

Think of it like a race track divided into 100-meter sections. The tens digit tells us which 10-meter segment we're in within that 100-meter section. Since 6 tens = 60, and 60 > 50, we're more than halfway between 400 and 500, so we round up.

The ones digit (7) only moves us 7 meters within our 10-meter segment, which doesn't change whether we're closer to 400 or 500.

Question: When I round 350 to the nearest 100, my teacher says it's 400, but it seems like it should be in the middle. Why do we round up?

Answer: You're absolutely right that 350 is exactly halfway between 300 and 400! This is called a "halfway case," and there is indeed a standard mathematical convention for handling it.

We round halfway cases (when the tens digit is exactly 5) up to the next hundred because:

  • Consistency: It creates a uniform rule that's easy to remember
  • Statistical fairness: In large sets of data, this prevents systematic bias toward lower numbers
  • Mathematical convention: It's the agreed-upon standard worldwide

So 350 rounds up to 400, just like 450 rounds up to 500, and 550 rounds up to 600.

Think of it as a tie-breaker: when there's a tie (exactly halfway), we always break toward the higher number.

Question: I have trouble remembering whether to round up or down. Is there a good memory trick?

Answer: Yes! Here are some helpful memory tricks for rounding:

  • "5 and above, let it fly": If the tens digit is 5, 6, 7, 8, or 9, round UP
  • "4 and below, let it go": If the tens digit is 0, 1, 2, 3, or 4, round DOWN
  • Number line visualization: Picture the number between two hundreds and see which one it's closer to

Another helpful approach is to think of the tens digit as a "decision maker":

  • 0-4: "I'm not strong enough to push up, so stay down" → Round down
  • 5-9: "I'm strong enough to push up!" → Round up

Practice with specific examples: 432 → tens digit is 3 (≤4) → round down to 400. 678 → tens digit is 7 (≥5) → round up to 700.