Rounding Place Value Exercises
1 Rounding to Tens
Exercise 1
Round 47 to the nearest ten.
Definition:
Rounding to tens: Finding the closest multiple of 10 to a given number by looking at the ones digit.
Method:
- Look at the ones digit
- If ones digit ≥ 5, round up
- If ones digit < 5, round down
47
Tens
Ones
4
7
47
(45-49 rounds up)
40
41
42
43
44
45
46
47
48
49
Since 7 ≥ 5, we round up to 50
Step 1: Identify the place to round to
We're rounding to the nearest ten, so we look at the tens place (4) and the ones place (7)
Step 2: Examine the ones digit
The ones digit is 7, which is greater than or equal to 5
Step 3: Apply the rounding rule
Since 7 ≥ 5, we round up to the next ten: 50
Final answer:
47 rounded to the nearest ten is 50
2 Rounding to Hundreds
Exercise 2
Round 1,473 to the nearest hundred.
1,473
Thousands
Hundreds
Tens
Ones
1
4
7
3
1,473
(1,450-1,499 rounds to 1,500)
1,400
1,410
1,420
1,430
1,440
1,450
1,460
1,470
1,480
1,490
Since 73 ≥ 50, we round up to 1,500
Step 1: Identify the place to round to
We're rounding to the nearest hundred, so we look at the hundreds place (4) and the tens and ones places (73)
Step 2: Examine the digits after hundreds
The tens and ones digits together are 73, which is greater than or equal to 50
Step 3: Apply the rounding rule
Since 73 ≥ 50, we round up to the next hundred: 1,500
Final answer:
1,473 rounded to the nearest hundred is 1,500
3 Rounding to Thousands
Exercise 3
Round 8,347 to the nearest thousand.
8,347
Thousands
Hundreds
Tens
Ones
8
3
4
7
8,347
(8,000-8,499 rounds down)
8,000
8,100
8,200
8,300
8,400
8,500
8,600
8,700
8,800
8,900
Since 347 < 500, we round down to 8,000
Step 1: Identify the place to round to
We're rounding to the nearest thousand, so we look at the thousands place (8) and the hundreds, tens, and ones places (347)
Step 2: Examine the digits after thousands
The hundreds, tens, and ones digits together are 347, which is less than 500
Step 3: Apply the rounding rule
Since 347 < 500, we round down to the same thousand: 8,000
Final answer:
8,347 rounded to the nearest thousand is 8,000
Rounding Rules & Strategies
Rounding to Nearest Ten
Look at the ones digit. If it's 5 or more, round up. If it's less than 5, round down. For example: 23 → 20, 27 → 30.
Rounding to Nearest Hundred
Look at the tens and ones digits together. If they form a number 50 or more, round up. If less than 50, round down. For example: 345 → 300, 367 → 400.
Rounding to Nearest Thousand
Look at the hundreds, tens, and ones digits together. If they form a number 500 or more, round up. If less than 500, round down. For example: 2,499 → 2,000, 2,500 → 3,000.
Essential Rounding Rules:
• 5 Rule: If the digit to the right is 5 or more, round up
• Less than 5 Rule: If the digit to the right is less than 5, round down
• Keep Place Value: Only change the target place and higher places
Tip 1: Use a number line to visualize rounding.
Tip 2: Remember the "5 or more, raise the score" rule.
Tip 3: Always identify which place value you're rounding to first.
Rounding Rule: If digit ≥ 5, round up; If digit < 5, round down
Basic Rounding Formula
Visual Learning Guide
Rounding Patterns
Nearest Ten
Look at ones
Nearest Hundred
Look at tens & ones
Nearest Thousand
Look at hundreds, tens & ones
Nearest Ten Thousand
Look at thousands, hundreds, tens & ones
Rounding Process
Rounding Steps
1
Identify Place
2
Look Right
3
Compare
4
Round Up/Down
Important Note
When rounding, all digits to the right of the target place become zeros. For example, rounding 1,473 to nearest hundred gives 1,500.
Common Mistakes
Mistake: Looking at wrong digit position
Mistake: Forgetting to make lower digits zero
Mistake: Confusing "round up" vs "round down"
47 → 50, 147 → 100, 1,473 → 1,000
Rounding Examples
Complete Summary & Review
Definition of Rounding
Rounding is a mathematical process that simplifies numbers by replacing them with nearby values that are easier to work with. It involves finding the closest multiple of a specified place value (like 10, 100, or 1000) to a given number. This skill is essential for estimation and checking the reasonableness of answers.
Core Rules & Principles
Rule 1: The 5 Rule
If the digit to the right of the target place is 5 or greater, round up. If it's less than 5, round down. This is often remembered as "5 or more, raise the score."
Rule 2: Place Value Focus
When rounding to a specific place value, focus only on the digit immediately to the right of that place. All digits to the right of the target place become zeros after rounding.
Rule 3: Target Place Preservation
The target place value either stays the same (round down) or increases by 1 (round up). Higher place values remain unchanged.
Step-by-Step Method
Step 1: Identify the Target Place
Determine which place value you're rounding to (tens, hundreds, thousands, etc.).
Step 2: Locate the Critical Digit
Find the digit immediately to the right of the target place. This is the deciding digit.
Step 3: Compare and Decide
Compare the critical digit to 5. If it's 5 or greater, round up. If less than 5, round down.
Step 4: Adjust and Replace
Increase the target digit by 1 (if rounding up) or keep it the same (if rounding down). Replace all digits to the right with zeros.
Examples (Simple → Advanced)
Simple Example
Round 24 to nearest ten: Look at ones digit (4). Since 4 < 5, round down to 20.
Medium Example
Round 367 to nearest hundred: Look at tens and ones (67). Since 67 ≥ 50, round up to 400.
Advanced Example
Round 5,499 to nearest thousand: Look at hundreds, tens, and ones (499). Since 499 < 500, round down to 5,000.
Tips, Tricks & Common Pitfalls
Tip 1: Use Visualization
Draw a number line or imagine the number between two multiples to see which is closer.
Tip 2: Remember the Rhyme
"Four or less, let it rest. Five or more, raise the score!" helps remember the rounding rule.
Tip 3: Zero Everything Below
After rounding, all digits to the right of the target place become zeros.
Common Pitfall 1: Wrong Digit Focus
Don't look at the wrong place value when deciding whether to round up or down.
Common Pitfall 2: Forgetting Zeros
Always make digits to the right of the target place zero after rounding.
Key Notes for Memorization
- Remember: Look only at the digit to the right of your target place
- Rule: 5 or more rounds up, less than 5 rounds down
- Process: Change the target digit (if needed) and make lower digits zero
- Verification: Your rounded number should be close to the original
- Pattern: Each place value follows the same principle
Questions & Answers
Question: Why do we need to learn rounding? When will I use it in real life?
Answer: Rounding is incredibly useful in real life! Here are some examples:
- Estimating costs when shopping (rounding prices to the nearest dollar)
- Calculating approximate totals quickly
- Reading temperature, weight, or distance measurements
- Checking if your calculator answers make sense
- Budgeting and financial planning
Rounding helps you make quick estimates and check if your exact answers are reasonable!
Question: My child gets confused about which digit to look at when rounding. How can I help them remember?
Answer: Here are helpful strategies to remember which digit to look at:
- Teach them to underline the target place value
- Circle the digit immediately to the right
- Use the phrase "look right, decide, and change"
- Practice with visual aids like place value charts
- Start with simpler problems before advancing
Consistent practice with visual cues will build confidence!
Question: What happens when the digit I'm looking at is exactly 5? Do I round up or down?
Answer: When the digit is exactly 5, we round up! This is the standard mathematical convention:
- If the digit is 5, 6, 7, 8, or 9, round up
- If the digit is 0, 1, 2, 3, or 4, round down
- Remember: "5 or more, raise the score!"
For example: 25 rounds up to 30, and 155 rounds up to 160.