Using Place Value to Round Numbers - Grade 1

Learn to round numbers using place value: understanding tens and ones, number lines, and estimation through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Rounding to Nearest Ten
Exercise 1
Round 23 to the nearest ten using place value
Definition:

Rounding: Making a number simpler by changing it to the closest ten, hundred, or thousand.

Rounding method:
  1. Look at the ones digit
  2. If ones digit is 0, 1, 2, 3, or 4 → round down
  3. If ones digit is 5, 6, 7, 8, or 9 → round up
  4. Change the ones digit to 0
20
21
22
23
24
25
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27
28
29
30
10
10
1
1
1

23 = 2 tens + 3 ones

Number
23
Ones digit
3
Round to
20
Step 1: Identify the tens and ones

23 = 2 tens and 3 ones

Step 2: Look at the ones digit

The ones digit is 3

Step 3: Apply the rounding rule

Since 3 < 5, we round down to 20

Step 4: Change ones to zero

23 → 20

23 rounds to 20
Final answer:

23 rounded to the nearest ten is 20

Applied rules:

• Ones digit rule: 0-4 round down, 5-9 round up

• Place value: Only the ones digit determines rounding

• Simplification: Rounding makes numbers easier to work with

2 Rounding Up
Exercise 2
Round 37 to the nearest ten using place value
Definition:

Rounding up: When the ones digit is 5 or more, we round to the next higher ten.

30
31
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35
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37
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40
10
10
10
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1
1
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1

37 = 3 tens + 7 ones

Number
37
Ones digit
7
Round to
40
Step 1: Identify the tens and ones

37 = 3 tens and 7 ones

Step 2: Look at the ones digit

The ones digit is 7

Step 3: Apply the rounding rule

Since 7 ≥ 5, we round up to 40

Step 4: Change ones to zero

37 → 40

37 rounds to 40
Final answer:

37 rounded to the nearest ten is 40

Applied rules:

• Ones digit rule: 5 or more rounds up

• Next ten: Round up to the next multiple of 10

• Estimation: Rounding helps estimate totals quickly

3 Special Case: Five
Exercise 3
Round 45 to the nearest ten using place value
Definition:

Special case: When the ones digit is exactly 5, we round up to the next ten.

40
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50
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1

45 = 4 tens + 5 ones

Number
45
Ones digit
5
Round to
50
Step 1: Identify the tens and ones

45 = 4 tens and 5 ones

Step 2: Look at the ones digit

The ones digit is 5

Step 3: Apply the rounding rule for 5

When ones digit is exactly 5, we round up

Step 4: Change ones to zero

45 → 50

45 rounds to 50
Final answer:

45 rounded to the nearest ten is 50

Applied rules:

• Rule for 5: Numbers ending in 5 always round up

• Consistency: This ensures consistent rounding behavior

• Halfway point: 5 is exactly halfway between two tens

Rules and methods, laws,...
If ones digit ≥ 5, round up
If ones digit ≤ 4, round down
Rounding Rule
Round Down
0,1,2,3,4
Ones digits that round down
Round Up
5,6,7,8,9
Ones digits that round up
Change to Zero
Ones → 0
Always set ones to zero after rounding
Key definitions:

Rounding: The process of simplifying a number to the nearest ten, hundred, or thousand.

Place value: The value of a digit depends on its position in the number.

Tens digit: The digit in the tens place (second from the right).

Ones digit: The digit in the ones place (rightmost digit).

Estimation: Using rounded numbers to get approximate answers.

Complete methodology:
  1. Identify place values: Find the tens and ones digits
  2. Examine ones digit: Look at the rightmost digit
  3. Apply rounding rule: Use the 5-or-more rule
  4. Change ones to zero: Set the ones digit to 0
Tip 1: Remember: 5 is the "round up" number (think "5 or more, round up").
Tip 2: Use a number line to visualize which ten the number is closer to.
Tip 3: Practice with numbers that end in 4 and 5 to see the difference.
Tip 4: Always change the ones digit to 0 after rounding.
Key concept: Only the ones digit determines whether to round up or down.
Memory aid: "Four or less, let it rest (round down). Five or more, raise the score (round up)."
Essential rules to remember:

• If ones digit is 0, 1, 2, 3, or 4 → round down

• If ones digit is 5, 6, 7, 8, or 9 → round up

• When rounding, change the ones digit to 0

• The tens digit stays the same when rounding down

• The tens digit increases by 1 when rounding up

Solution: Exercises 4 to 5
4 Problem Solving
Exercise 4
Sarah collected 68 seashells. About how many tens of seashells did she collect? Round to the nearest ten.
Definition:

Estimation: Using rounding to get an approximate answer that's close enough for practical purposes.

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68 = 6 tens + 8 ones

Number
68
Ones digit
8
Round to
70
Step 1: Identify the tens and ones

68 = 6 tens and 8 ones

Step 2: Look at the ones digit

The ones digit is 8

Step 3: Apply the rounding rule

Since 8 ≥ 5, we round up to 70

Step 4: Answer the question

Sarah collected about 70 seashells (7 tens)

About 70 seashells (7 tens)
Final answer:

Sarah collected about 70 seashells (7 tens).

Applied rules:

• Real-world application: Rounding helps with estimation

• Contextual answer: Relate the rounded number back to the problem

• Verification: 68 is closer to 70 than to 60

5 Number Puzzles
Exercise 5
I am a number between 30 and 40. When I am rounded to the nearest ten, I become 30. What number could I be?
Definition:

Number puzzles: Problems that require understanding of rounding rules and number relationships.

30
31
32
33
34
35
36
37
38
39
40
34 rounds down to 30
Range
30-39
Round to
30
Possible numbers
30, 31, 32, 33, 34
Step 1: Identify the range

Numbers between 30 and 40: 30, 31, 32, 33, 34, 35, 36, 37, 38, 39

Step 2: Apply the rounding rule

For a number to round down to 30, its ones digit must be ≤ 4

Step 3: Find numbers with ones digit ≤ 4

30 (ones = 0), 31 (ones = 1), 32 (ones = 2), 33 (ones = 3), 34 (ones = 4)

Step 4: Verify the answer

35 and above would round up to 40, so they don't work

30, 31, 32, 33, or 34
Final answer:

The number could be 30, 31, 32, 33, or 34.

Applied rules:

• Logic reasoning: Use constraints to narrow down possibilities

• Systematic approach: Check each possibility against the condition

• Verification: Confirm that all answers satisfy the requirements

Complete Summary: Using Place Value to Round Numbers
Round(X) = Tens digit + (Ones ≥ 5 ? 1 : 0) × 10
Rounding Formula
Key definitions:

Rounding: The process of approximating a number to the nearest specified place value.

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

Estimation: Using rounded numbers to get approximate answers quickly.

Tens place: The second digit from the right in a two-digit number.

Ones place: The rightmost digit in a number.

Complete methodology:
  1. Identify the target place: Determine which place value to round to
  2. Locate the determining digit: Find the digit in the place being rounded
  3. Apply the rounding rule: Use the 5-or-more principle
  4. Adjust the number: Increase or decrease as needed
Tip 1: Think of rounding like climbing stairs: if you're halfway up, you go to the next step.

Tip 2: Remember the rhyme: "Four or less, let it rest. Five or more, raise the score."

Tip 3: Use a number line to see which ten the number is closer to.

Tip 4: Always set the ones digit to 0 after rounding.

Common mistake: Forgetting to change the ones digit to 0 after rounding.

Success strategy: Focus only on the ones digit - ignore other digits when rounding to tens.

Essential formulas to remember:

• If ones digit ≤ 4: round down (keep tens digit same)

• If ones digit ≥ 5: round up (increase tens digit by 1)

• Always set ones digit to 0 after rounding

• When rounding up: XX → (X+1)0

• When rounding down: XX → X0

Rounding Numbers Guide

📊
Rounding Rules

Round down: Ones digit 0, 1, 2, 3, 4

Round up: Ones digit 5, 6, 7, 8, 9

Change ones to 0: Always after rounding

Examples

Round down: 21→20, 22→20, 23→20, 24→20

Round up: 25→30, 26→30, 27→30, 28→30, 29→30

Key Points

Only ones matter: When rounding to tens, only the ones digit counts

5 rounds up: This is the halfway point rule

Estimation tool: Rounding helps make numbers easier to work with

Rounding Problem-Solving
1
Identify
2
Examine
3
Apply
4
Change
Master Rounding: Build Strong Estimation Skills!

Questions & Answers

Question: Why do we round numbers? Don't we want exact answers?

Answer: Great question! We round numbers for several reasons:

  • Quick estimates: Sometimes we just need an approximate answer
  • Easier calculations: It's easier to add 20 + 30 than 23 + 27
  • Real-world applications: We often don't need exact precision
  • Checking work: Rounding helps verify if our exact answers make sense

Exact answers are important for precise work, but rounding helps us understand numbers better!

Question: How can I help my child practice rounding numbers at home?

Answer: Here are some engaging activities for home practice:

  • Shopping: Round prices to the nearest dollar when shopping
  • Number line: Draw a number line and have your child identify which ten numbers are closer to
  • Household items: Count items and round the totals
  • Age games: Round family members' ages to the nearest ten
  • Time estimation: Round minutes to the nearest 10 or 15

Make it a game - the more practice, the more natural it becomes!

Question: Why does 5 always round up? Shouldn't it round down since it's in the middle?

Answer: You're right that 5 is in the middle! Mathematicians decided that 5 always rounds up to keep things consistent:

  • This prevents bias toward rounding down
  • It creates a simple, clear rule: 5 or more rounds up
  • It makes calculations more predictable
  • It helps with estimating - it's better to round up than down when uncertain

Think of it as a tie-breaker - when there's a tie, we always go up!