Solved Exercises on Place Value and Rounding in Grade 4

Master place value and rounding: identifying place values, rounding to nearest tens/hundreds/thousands, and mixed problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Place value identification
Exercise 1
In the number 7,842, what is the value of the digit 8? Round 7,842 to the nearest hundred.
Definition:

Place value: The value of a digit based on its position in the number. Rounding: Finding the closest multiple of a given place value.

Method:
  1. Identify the position of the target digit
  2. Recognize the place value of that position
  3. Multiply the digit by the value of its position
  4. For rounding, look at the digit to the right of the rounding place
Thousands
7
Hundreds
8
Tens
4
Ones
2
Step 1: Identify the position

In 7,842, the digit 8 is in the hundreds place

Step 2: Calculate the place value

Digit value = 8 × 100 = 800

Step 3: Round to nearest hundred

Look at the tens digit (4). Since 4 < 5, we round down

7,842 rounded to the nearest hundred is 7,800

8 × 100 = 800
7,842 → 7,800
Final answer:

The value of the digit 8 is 800. 7,842 rounded to the nearest hundred is 7,800.

Applied rules:

• Place value rule: Digit value = Digit × Place value

• Rounding rule: If digit to the right is ≥ 5, round up; if < 5, round down

• Position recognition: Count positions from right to left

Tip: When rounding, only look at the digit immediately to the right of your rounding place.
2 Rounding to different places
Exercise 2
Round 5,678 to the nearest ten, hundred, and thousand.
Definition:

Rounding to different places: Applying the same rounding rule to different place values in the same number.

Thousands
5
Hundreds
6
Tens
7
Ones
8
Round to Tens
5,678 → 5,680
→
Round to Hundreds
5,678 → 5,700
→
Round to Thousands
5,678 → 6,000
Step 1: Round to nearest ten

Look at ones digit (8). Since 8 ≥ 5, round up: 5,678 → 5,680

Step 2: Round to nearest hundred

Look at tens digit (7). Since 7 ≥ 5, round up: 5,678 → 5,700

Step 3: Round to nearest thousand

Look at hundreds digit (6). Since 6 ≥ 5, round up: 5,678 → 6,000

To tens: 5,678 → 5,680
To hundreds: 5,678 → 5,700
To thousands: 5,678 → 6,000
Final answer:

5,678 rounded to the nearest ten is 5,680, to the nearest hundred is 5,700, and to the nearest thousand is 6,000.

Applied rules:

• Consistent rounding rule: Same rule applies to all place values

• Target digit focus: Always look at the digit to the right of the rounding place

• Adjustment principle: Increase the target digit by 1 if rounding up

Tip: The same number can have different rounded values depending on the place you're rounding to.
3 Mixed place value and rounding
Exercise 3
What is the value of the digit 3 in 34,567? Then round 34,567 to the nearest thousand.
Definition:

Mixed operations: Combining place value identification with rounding in a single problem.

Ten Thousands
3
Thousands
4
Hundreds
5
Tens
6
Ones
7
Step 1: Identify the position of digit 3

In 34,567, the digit 3 is in the ten thousands place

Step 2: Calculate the place value

Digit value = 3 × 10,000 = 30,000

Step 3: Round to nearest thousand

Look at the hundreds digit (5). Since 5 ≥ 5, round up: 34,567 → 35,000

3 × 10,000 = 30,000
34,567 → 35,000
Final answer:

The value of the digit 3 is 30,000. 34,567 rounded to the nearest thousand is 35,000.

Applied rules:

• Sequential processing: Handle each part of the problem separately

• Place value hierarchy: Larger positions have larger values

• Rounding consistency: Same rule applies regardless of number size

Tip: Break complex problems into smaller, manageable steps.
Place Value and Rounding Rules
Digit Value = Digit × Place Value
Place Value Formula
Ones Place
× 1
Value = Digit × 1
Tens Place
× 10
Value = Digit × 10
Hundreds Place
× 100
Value = Digit × 100
Thousands Place
× 1,000
Value = Digit × 1,000
Rounding Rule
≥ 5 UP
< 5 DOWN
Key definitions:

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

Rounding: Replacing a number with an approximate value that has a simpler representation

Digit: Any symbol (0-9) used to make up a number

Place Value Method:
  1. Locate the digit: Find the target digit in the number
  2. Identify position: Count from right to left (ones, tens, hundreds...)
  3. Apply formula: Multiply digit by place value
Rounding Method:
  1. Determine rounding place: Decide which place to round to
  2. Look at next digit: Check the digit to the right of the rounding place
  3. Apply rule: If ≥ 5, round up; if < 5, round down
  4. Set trailing zeros: Replace all digits to the right with zeros
Tip 1: Start counting positions from the right (ones, tens, hundreds...).
Tip 2: When rounding, only look at the digit immediately to the right.
Tip 3: The same digit has different values in different positions.
Tip 4: Remember: 5 or more, raise the score; 4 or less, let it rest.
Common errors: Confusing place names, rounding to wrong place, forgetting trailing zeros.
Memorization trick: "The bigger the place, the bigger the value" - each position to the left is 10 times greater.
Place Value System:

• Rightmost position: Ones (1)

• Next position left: Tens (10)

• Next position left: Hundreds (100)

• Next position left: Thousands (1,000)

• Next position left: Ten Thousands (10,000)

• Next position left: Hundred Thousands (100,000)

Rounding Rules:

• Look at the digit to the right of the rounding place

• If digit ≥ 5 (5, 6, 7, 8, 9), round UP

• If digit < 5 (0, 1, 2, 3, 4), round DOWN

• Change the target digit by +1 if rounding up

• Set all digits to the right to zero

Solution: Exercises 4 to 5
4 Advanced rounding
Exercise 4
Round 12,549 to the nearest ten, hundred, and thousand. Explain why the rounded values differ.
Definition:

Advanced rounding: Rounding the same number to different place values and understanding the differences.

Ten Thousands
1
Thousands
2
Hundreds
5
Tens
4
Ones
9
Round to Tens
12,549 → 12,550
→
Round to Hundreds
12,549 → 12,500
→
Round to Thousands
12,549 → 13,000
Step 1: Round to nearest ten

Look at ones digit (9). Since 9 ≥ 5, round up: 12,549 → 12,550

Step 2: Round to nearest hundred

Look at tens digit (4). Since 4 < 5, round down: 12,549 → 12,500

Step 3: Round to nearest thousand

Look at hundreds digit (5). Since 5 ≥ 5, round up: 12,549 → 13,000

Step 4: Explanation of differences

Each rounding focuses on a different place value, so different digits determine the rounding direction.

To tens: 12,549 → 12,550
To hundreds: 12,549 → 12,500
To thousands: 12,549 → 13,000
Final answer:

12,549 rounded to the nearest ten is 12,550, to the nearest hundred is 12,500, and to the nearest thousand is 13,000.

Applied rules:

• Consistent rounding rule: Same rule applies to all place values

• Target-specific focus: Each rounding considers a different digit

• Progressive approximation: Larger rounding places result in less precision

5 Real-world application
Exercise 5
A school has 1,847 students. Round this number to the nearest hundred to estimate the population. What is the value of the digit 8?
Definition:

Real-world application: Using place value and rounding to solve practical problems involving estimation.

Thousands
1
Hundreds
8
Tens
4
Ones
7
Step 1: Identify the position of digit 8

In 1,847, the digit 8 is in the hundreds place

Step 2: Calculate the place value

Digit value = 8 × 100 = 800

Step 3: Round to nearest hundred

Look at the tens digit (4). Since 4 < 5, round down: 1,847 → 1,800

Step 4: Interpret the result

The school has approximately 1,800 students when rounded to the nearest hundred.

8 × 100 = 800
1,847 → 1,800
Final answer:

The value of the digit 8 is 800. The school has approximately 1,800 students when rounded to the nearest hundred.

Applied rules:

• Practical rounding: Estimation helps simplify large numbers

• Place value recognition: Position determines digit value

• Real-world relevance: Rounding is useful for approximations

Place Value and Rounding Summary
Comprehensive Learning Summary

Definitions and Key Concepts

Place Value: The value of a digit based on its position in a number. Each position represents a power of 10.

Rounding: The process of replacing a number with an approximate value that has a simpler representation.

Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers.

Number: A mathematical object used to count, measure, and label.

Core Rules and Principles

Place Value Rule: Digit Value = Digit × Place Value

Rounding Rule: Look at the digit to the right of the rounding place. If ≥ 5, round up. If < 5, round down.

Base-10 System: Each place value is 10 times the previous one.

Step-by-Step Methods

Place Value Identification:

  1. Locate the target digit in the number
  2. Count positions from right to left (ones, tens, hundreds, thousands...)
  3. Identify the place value of that position
  4. Multiply the digit by its place value

Rounding Process:

  1. Determine which place value to round to
  2. Identify the digit in that place
  3. Look at the digit immediately to the right
  4. If right digit ≥ 5, increase the target digit by 1 (round up)
  5. If right digit < 5, keep the target digit the same (round down)
  6. Replace all digits to the right with zeros

Examples (Simple to Advanced)

Simple Example: In 234, the value of 3 is 3 × 10 = 30. Round 234 to nearest ten: 234 → 230.

Intermediate Example: In 5,678, the value of 6 is 6 × 100 = 600. Round to nearest hundred: 5,678 → 5,700.

Advanced Example: In 12,549, the value of 2 is 2 × 1,000 = 2,000. Round to nearest thousand: 12,549 → 13,000.

Tips and Memory Aids

"5 or more, raise the score; 4 or less, let it rest" - This rhyme helps remember the rounding rule.

Always start counting positions from the right - ones, tens, hundreds, thousands...

Same digit, different value - The digit 5 in 500 (5 × 100 = 500) vs 50 (5 × 10 = 50) shows how position affects value.

Common Mistakes to Avoid

Confusing place names - Mixing up tens and hundreds positions.

Looking at wrong digit when rounding - Only look at the digit immediately to the right of the rounding place.

Forgetting trailing zeros - After rounding, all digits to the right of the rounding place become zeros.

Key Takeaways for Memorization

• Place value depends on position, not the digit itself

• Each position to the left is 10 times greater than the position to its right

• Rounding simplifies numbers while keeping them close to the original value

• Practice with different numbers to build confidence and accuracy

Digit Value = Digit × Place Value
Core Formula
Key definitions:

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

Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers

Number: A mathematical object used to count, measure, and label

Complete methodology:
  1. Identify the target digit: Locate the specific digit in question
  2. Determine the position: Count positions from right to left (ones, tens, hundreds...)
  3. Recognize the place value: Know the value associated with each position
  4. Calculate the value: Multiply the digit by its place value
  5. Verify the answer: Ensure the calculated value makes logical sense
Tip 1: Always start counting positions from the rightmost digit (ones place).
Tip 2: Each position to the left is 10 times greater than the position to its right.
Tip 3: The same digit has different values depending on its position (e.g., 5 in 500 vs 5 in 50).
Tip 4: Use commas to separate large numbers into groups of three for easier reading.
Common errors: Miscounting positions, confusing place names, forgetting to multiply by place value.
Memory aid: "O-H-T-T-T-H" - Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands.
Place Value Rules:

• Base-10 system: Each place value is 10 times the previous one

• Position matters: Same digit has different values in different positions

• Right-to-left counting: Positions increase from right to left

• Zero as placeholder: Zeros hold place value positions

• Grouping convention: Commas separate every three digits starting from the right

Rounding Rules:

• Look right rule: Always examine the digit to the right of the rounding place

• 5 or more: Round up by increasing the target digit by 1

• Less than 5: Round down by keeping the target digit the same

• Zero replacement: Set all digits to the right to zero after rounding

Questions & Answers

Question: I'm confused about when to round up and when to round down. How do I remember which is which?

Answer: Here's a helpful memory trick: "5 or more, raise the score; 4 or less, let it rest!"

When rounding, you always look at the digit to the right of the place you're rounding to:

  • If that digit is 5, 6, 7, 8, or 9 (5 or more), you ROUND UP by adding 1 to the target digit
  • If that digit is 0, 1, 2, 3, or 4 (less than 5), you ROUND DOWN by keeping the target digit the same

Examples:

  • Round 47 to nearest ten: Look at 7 (right of tens place). Since 7 ≥ 5, round up: 47 → 50
  • Round 43 to nearest ten: Look at 3 (right of tens place). Since 3 < 5, round down: 43 → 40
  • Round 45 to nearest ten: Look at 5 (right of tens place). Since 5 ≥ 5, round up: 45 → 50

Remember: 5 is the "magic number" - it's the dividing line between rounding up and down!

Question: Why do we need to learn place value before rounding? Are they connected?

Answer: Yes, place value and rounding are very closely connected! Understanding place value is essential for rounding because:

  • You need to identify positions: When rounding, you must know which place value you're rounding to (tens, hundreds, thousands, etc.)
  • You need to locate digits: You must find the specific digit in the rounding place and the digit immediately to its right
  • You need to understand value relationships: Each position is 10 times greater than the position to its right, which affects how rounding works

Think of it like this: Place value tells you WHERE the digits are and WHAT they're worth, and rounding uses that information to simplify the number. You can't round properly without knowing where each digit sits in the number!

Example: To round 3,472 to the nearest hundred, you need to:

  • Identify the hundreds place (4)
  • Identify the digit to its right (7)
  • Apply the rounding rule based on that digit

Question: When I round a number, do I change the original number permanently, or is it just for estimating?

Answer: Rounding creates an APPROXIMATE value of the original number, not a permanent change. The original number stays the same! Rounding is mainly used for:

  • Estimating: Making quick calculations easier
  • Simplifying: Working with large numbers that are hard to handle
  • Approximating: Getting close enough answers for practical purposes

For example, if you have 1,987 students in a school, you might round to 2,000 for a quick estimate, but the actual number is still 1,987. The rounded number is just easier to work with mentally.

The relationship is: Original number → Rounding process → Approximate (rounded) number

Both numbers exist - the original for precise work and the rounded version for estimation and mental math!

Examples:

  • Original: 1,987 → Rounded: 2,000 (for estimation)
  • Original: 243 → Rounded: 240 (to nearest ten)
  • Original: 8,456 → Rounded: 8,000 (to nearest thousand)