Comprehensive Rounding and Place Value Worksheet for Grade 4

Complete worksheet with exercises on place value identification, rounding to different places, number comparison, and expanded form conversion.

Worksheet Summary & Key Concepts
Comprehensive Summary:

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

Rounding: Approximating numbers to make them easier to work with by replacing them with nearby numbers that are multiples of 10, 100, 1000, etc.

Key Definitions:

Digit: Any of the numerals 0-9 used to form numbers.

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, etc.).

Face Value: The actual value of a digit regardless of its position.

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

Expanded Form: Writing a number as the sum of the value of each digit.

Standard Form: Writing a number in the normal way using digits.

Core Rules and Laws:

• Place Value Pattern: Ones, Tens, Hundreds, Thousands, Ten Thousands... Each place is 10 times the previous place

• Rounding Rule: Look at the digit to the right of your target place: 5 or more rounds UP, 4 or less rounds DOWN

• Zero Replacement: After rounding, all digits to the right of the target place become zeros

• Comparison Method: Compare numbers from left to right, starting with the highest place value

• Expanded Form: Each digit multiplied by its place value and added together

Step-by-Step Methods:
  1. Identifying Place Value: Locate the position of each digit from right to left
  2. Understanding Relationships: Know that each place is 10 times the next lower place
  3. Applying Rounding Rules: Look at the digit to the right of the target place
  4. Verifying Results: Check if rounded number makes sense in context
  5. Comparing Numbers: Start from the leftmost digit and work right
  6. Writing Expanded Form: Multiply each digit by its place value and add
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
Tip 5: Use a number line to visualize rounding when unsure
Common Mistakes: Confusing place value with face value, forgetting to change digits to zero after rounding, misidentifying target place.
Memory Aids: "Pancakes have 5 letters, so 5 or more rounds up", "Tens place is for the 2nd digit from the right".
🏠 Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones
Place Value Chart Structure
Worksheet Exercises
Exercise 1: Place Value Identification
Exercise 1
For each number, identify the place value of the underlined digit:
a) 87,342 (underline the 7)
b) 52,691 (underline the 2)
c) 94,058 (underline the 0)
Solutions:

a) In 87,342, the 7 is in the thousands place. Its value is 7 × 1,000 = 7,000

b) In 52,691, the 2 is in the thousands place. Its value is 2 × 1,000 = 2,000

c) In 94,058, the 0 is in the hundreds place. Its value is 0 × 100 = 0

Exercise 2: Rounding to Different Places
Exercise 2
Round each number to the specified place:
a) 63,847 to the nearest ten
b) 49,256 to the nearest hundred
c) 71,583 to the nearest thousand
Solutions:

a) 63,847 to nearest ten: Target is tens place (4), deciding digit is ones place (7). Since 7 ≥ 5, round UP → 63,850

b) 49,256 to nearest hundred: Target is hundreds place (2), deciding digit is tens place (5). Since 5 ≥ 5, round UP → 49,300

c) 71,583 to nearest thousand: Target is thousands place (1), deciding digit is hundreds place (5). Since 5 ≥ 5, round UP → 72,000

Exercise 3: Number Comparison
Exercise 3
Compare each pair of numbers using >, <, or =:
a) 54,721 _____ 54,271
b) 83,649 _____ 83,649
c) 62,158 _____ 62,518
Solutions:

a) 54,721 > 54,271 (compare from left: same in ten thousands and thousands, then 7 > 2 in hundreds)

b) 83,649 = 83,649 (identical numbers)

c) 62,158 < 62,518 (same in ten thousands and thousands, then 1 < 5 in hundreds)

Advanced Practice Problems
Advanced Exercise 1
Advanced Exercise 1
Write each number in expanded form:
a) 75,392
b) 48,061
c) 92,740
Solutions:

a) 75,392 = 70,000 + 5,000 + 300 + 90 + 2

b) 48,061 = 40,000 + 8,000 + 0 + 60 + 1

c) 92,740 = 90,000 + 2,000 + 700 + 40 + 0

Advanced Exercise 2
Advanced Exercise 2
Round each number to the nearest ten, hundred, and thousand:
a) 58,743
b) 92,568
c) 34,821
Solutions:

a) 58,743: Nearest ten = 58,740, Nearest hundred = 58,700, Nearest thousand = 59,000

b) 92,568: Nearest ten = 92,570, Nearest hundred = 92,600, Nearest thousand = 93,000

c) 34,821: Nearest ten = 34,820, Nearest hundred = 34,800, Nearest thousand = 35,000

Advanced Exercise 3
Advanced Exercise 3
Order these numbers from least to greatest:
63,847, 63,487, 63,748, 63,478
Solution Process:

All numbers have 6 in ten thousands and 3 in thousands, so compare hundreds place:

63,487 and 63,478 have 4 in hundreds

Between 63,487 and 63,478: 7 < 8 in tens, so 63,478 < 63,487

Between 63,748 and 63,847: 7 < 8 in hundreds, so 63,748 < 63,847

Order: 63,478 < 63,487 < 63,748 < 63,847

Final Answer:

63,478, 63,487, 63,748, 63,847

Advanced Exercise 4
Advanced Exercise 4
Create the largest and smallest possible 5-digit numbers using the digits: 3, 7, 1, 9, 4
Solution Process:

To make the largest number, arrange digits from greatest to least: 97,431

To make the smallest number, arrange digits from least to greatest: 13,479

Note: We cannot start with 0 (which we don't have anyway), so 1 is the smallest possible first digit

Final Answer:

Largest: 97,431, Smallest: 13,479

Questions & Answers

Question: When I round 9,999 to the nearest ten, I get confused because 9 + 1 = 10, but there's no room for 10 in that place. How do I handle this?

Answer: This is a common challenge! When rounding causes a digit to become 10, it carries over to the next higher place value:

  • When rounding 9,999 to the nearest ten:
  • Tens digit is 9, ones digit is 9 (≥ 5, so round up)
  • 9 tens + 1 ten = 10 tens = 1 hundred
  • This adds 1 to the hundreds place: 9 hundreds + 1 = 10 hundreds = 1 thousand
  • This adds 1 to the thousands place: 9 thousands + 1 = 10 thousands = 1 ten thousand
  • So 9,999 rounded to the nearest ten is 10,000

The key is that when a place value reaches 10, it converts to 1 unit of the next higher place value, just like in regular addition!

Question: How can I help my child practice place value and rounding at home? Are there fun activities we can do together?

Answer: Here are engaging activities to practice at home:

  1. Number Line Walks: Draw a number line and have your child walk to the nearest 10 or 100
  2. Place Value Charts: Use base-10 blocks or draw charts to visualize each place value
  3. Real-world Rounding: Round grocery prices, distances, or temperatures
  4. Card Games: Use playing cards to create numbers and practice rounding
  5. Estimation Challenges: Estimate quantities around the house and then count to check

Make it a game! Consistent practice with fun activities will build confidence and understanding!

Question: I sometimes forget which place is which when I'm working with big numbers. How can I remember the order?

Answer: Here are memory aids for place value order:

  • Starting from the right: On-ES, T-ENS, H-UNDREDS, TH-OUSANDS, TE-N THOUSANDS, H-UNDR-ED TH-OUSANDS
  • Pattern Recognition: Each place is 10 times the previous place
  • Visual Aid: Draw a place value chart and fill in the names
  • Practice Counting: Say the place values out loud: ones, tens, hundreds, thousands...

Remember: the pattern continues infinitely in both directions! The names repeat every three places: thousands, millions, billions, etc.