Solved Exercises on Rounding and Place Value Activities in Grade 4

Master place value and rounding: identify digit positions, round numbers to nearest tens/hundreds/thousands, compare values through these 5 detailed exercises.

Rules and methods, laws,...
🏠 Thousands | Hundreds | Tens | Ones | Tenths
Place Value Chart
Rounding Rule
5 or more → Round UP
Less than 5 → Round DOWN
Place Value
Each position = 10× previous
Tens = 10× Ones, Hundreds = 10× Tens
Comparison
Compare left to right
Start with highest place value
Key definitions:

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

Rounding: Approximating a number to the nearest ten, hundred, or thousand

Digit: Any of the numerals 0-9

Complete methodology:
  1. Identify place value: Locate the position of each digit
  2. Understand relationships: Know that each place is 10 times the next lower place
  3. Apply rounding rules: Look at the digit to the right of the target place
  4. Verify results: Check if rounded number makes sense
Tip 1: Remember "5 or more, raise the score; 4 or less, let it rest"
Tip 2: Draw a place value chart to visualize digit positions
Tip 3: Always underline the digit you're rounding to
Tip 4: Replace digits to the right with zeros after rounding
Common errors: Confusing place value with face value, forgetting to change digits to zero after rounding.
Exam preparation: Practice with large numbers, memorize rounding rules, work with word problems.
Rules to know by heart:

• Place Value Pattern: Ones, Tens, Hundreds, Thousands, Ten Thousands...

• Rounding Rule: Look at digit to the right - 5+ rounds up, 4- rounds down

• Value Relationship: Each place is 10 times the previous place

• Zero Replacement: Digits to the right become zeros after rounding

Solution: Exercises 1 to 3
1 Place Value Identification
Exercise 1
In the number 5,837, identify the place value of each digit and write the expanded form.
Definition:

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

Place value identification method:
  1. Start from the rightmost digit (ones place)
  2. Move left, increasing the place value by powers of 10
  3. Write the expanded form by multiplying each digit by its place value
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
5
8
3
7
Step 1: Identify each digit's place

5 is in the thousands place = 5 × 1,000 = 5,000

8 is in the hundreds place = 8 × 100 = 800

3 is in the tens place = 3 × 10 = 30

7 is in the ones place = 7 × 1 = 7

Step 2: Write expanded form

5,837 = 5,000 + 800 + 30 + 7

Step 3: Express in multiplication form

5,837 = (5 × 1,000) + (8 × 100) + (3 × 10) + (7 × 1)

5,837 = 5,000 + 800 + 30 + 7
Final answer:

5 is in thousands place (value: 5,000), 8 in hundreds (800), 3 in tens (30), 7 in ones (7)

Expanded form: 5,837 = 5,000 + 800 + 30 + 7

Applied rules:

• Positional notation: Each position has specific value

• Place value pattern: Each place is 10 times the previous

• Expanded form: Shows value of each digit separately

2 Rounding to Nearest Ten
Exercise 2
Round 4,867 to the nearest ten.
Definition:

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

Rounding to nearest ten method:
  1. Identify the tens digit (second from right)
  2. Look at the ones digit (rightmost)
  3. If ones ≥ 5, round up; if ones ≤ 4, round down
  4. Change all digits to the right to zero
Thousands
Hundreds
Tens
Ones
4
8
6
7
↓
Step 1: Identify the target place

We want to round to the nearest ten, so look at the tens digit (6)

Step 2: Look at the deciding digit

The digit to the right of tens is the ones digit (7)

Step 3: Apply rounding rule

Since 7 ≥ 5, we round up. Increase the tens digit by 1 (6 + 1 = 7)

Step 4: Replace smaller place values

Change all digits to the right of tens to zero: 4,870

4,867 rounded to the nearest ten = 4,870
Final answer:

4,867 rounded to the nearest ten is 4,870

Applied rules:

• Rounding rule: 5 or more rounds up, 4 or less rounds down

• Target place: Identify which place to round to

• Deciding digit: Look at digit immediately to the right

3 Rounding to Nearest Hundred
Exercise 3
Round 7,428 to the nearest hundred.
Definition:

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

Rounding to nearest hundred method:
  1. Identify the hundreds digit (third from right)
  2. Look at the tens digit (second from right)
  3. If tens ≥ 5, round up; if tens ≤ 4, round down
  4. Change all digits to the right to zero
Thousands
Hundreds
Tens
Ones
7
4
2
8
↓
Step 1: Identify the target place

We want to round to the nearest hundred, so look at the hundreds digit (4)

Step 2: Look at the deciding digit

The digit to the right of hundreds is the tens digit (2)

Step 3: Apply rounding rule

Since 2 ≤ 4, we round down. Keep the hundreds digit the same (4)

Step 4: Replace smaller place values

Change all digits to the right of hundreds to zero: 7,400

7,428 rounded to the nearest hundred = 7,400
Final answer:

7,428 rounded to the nearest hundred is 7,400

Applied rules:

• Rounding rule: 5 or more rounds up, 4 or less rounds down

• Target place: Identify which place to round to

• Deciding digit: Look at digit immediately to the right

Solution: Exercises 4 to 5
4 Comparing Numbers Using Place Value
Exercise 4
Compare 3,572 and 3,527. Which is greater?
Definition:

Comparing numbers: Determining which number is greater, lesser, or equal by comparing digits from left to right.

Number comparison method:
  1. Compare digits starting from the leftmost (highest place value)
  2. If digits are equal, move to the next place value
  3. The first place where digits differ determines the greater number
Number 1: 3,572
Thousands
Hundreds
Tens
Ones
Number 2: 3,527
3
5
7
2
3
5
2
7
Step 1: Compare thousands place

Both numbers have 3 in thousands place, so continue to next place

Step 2: Compare hundreds place

Both numbers have 5 in hundreds place, so continue to next place

Step 3: Compare tens place

3,572 vs 3,527 → 7 > 2

Step 4: Make conclusion

Since 7 > 2 in the tens place, 3,572 > 3,527

3,572 > 3,527
Final answer:

3,572 is greater than 3,527

Applied rules:

• Left-to-right comparison: Start with highest place value

• Place value importance: Higher places matter more

• Difference detection: First differing digit determines outcome

5 Rounding to Nearest Thousand
Exercise 5
Round 8,642 to the nearest thousand.
Definition:

Rounding to nearest thousand: Finding the closest multiple of 1,000 to a given number.

Rounding to nearest thousand method:
  1. Identify the thousands digit (fourth from right)
  2. Look at the hundreds digit (third from right)
  3. If hundreds ≥ 5, round up; if hundreds ≤ 4, round down
  4. Change all digits to the right to zero
Thousands
Hundreds
Tens
Ones
8
6
4
2
↓
Step 1: Identify the target place

We want to round to the nearest thousand, so look at the thousands digit (8)

Step 2: Look at the deciding digit

The digit to the right of thousands is the hundreds digit (6)

Step 3: Apply rounding rule

Since 6 ≥ 5, we round up. Increase the thousands digit by 1 (8 + 1 = 9)

Step 4: Replace smaller place values

Change all digits to the right of thousands to zero: 9,000

8,642 rounded to the nearest thousand = 9,000
Final answer:

8,642 rounded to the nearest thousand is 9,000

Applied rules:

• Rounding rule: 5 or more rounds up, 4 or less rounds down

• Target place: Identify which place to round to

• Deciding digit: Look at digit immediately to the right

Questions & Answers

Question: I get confused when rounding numbers like 5,499 to the nearest hundred. When I look at the tens place (9), it's more than 5, so I round up the hundreds place (4) to 5, but then I have 5,599. That doesn't seem right!

Answer: Great question! You're on the right track with the rounding rule, but there's one important step you missed. When rounding 5,499 to the nearest hundred:

  • Hundreds digit is 4, tens digit is 9
  • Since 9 ≥ 5, you round UP: 4 + 1 = 5
  • Here's the key: Change ALL digits to the right of the hundreds place to zero
  • So 5,499 becomes 5,500 (not 5,599)

The mistake was keeping the tens and ones digits instead of changing them to zeros. When rounding to a specific place, everything to the right becomes zero!

Question: My child is struggling with place value. They understand that 5 in the hundreds place means 500, but they have trouble with larger numbers like 23,456. How can I help them visualize this better?

Answer: Try these visualization strategies for 23,456:

  1. Draw a place value chart: Write each digit under its correct heading
  2. Use base-10 blocks: Show 2 ten-thousands blocks, 3 thousands blocks, etc.
  3. Break it down: 20,000 + 3,000 + 400 + 50 + 6
  4. Read it aloud: "Twenty-three thousand, four hundred fifty-six"

You can also use money as an analogy: $23,456 has 2 ten-thousands, 3 thousands, 4 hundreds, 5 tens, and 6 ones. This connects abstract numbers to something concrete!

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

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

  • Shopping: Rounding prices to estimate total costs ($2.99 becomes $3)
  • Time: Saying "about 3 hours" instead of "2 hours and 58 minutes"
  • Population: "About 8 million people live in NYC" (not exact count)
  • Budgeting: Rounding income/expenses to make calculations easier
  • Measurements: "About 5 feet tall" instead of exact inches

Rounding helps us make quick estimates and understand large numbers more easily!