Solved Exercises on Comparing Numbers to 1000 in Grade 2

Master comparing numbers up to 1000: place value comparison, greater than less than, ordering numbers through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Place Value Comparison
Exercise 1
Compare 425 and 387. Which number is greater?
Definition:

Place value: Each digit in a number has a value based on its position (hundreds, tens, ones)

Comparison method:
  1. Compare digits from left to right (highest place value first)
  2. If hundreds are different, compare hundreds
  3. If hundreds are the same, compare tens
  4. If tens are the same, compare ones
Numbers
425 vs 387
Comparison
425 > 387
Step 1: Compare hundreds place

425 has 4 hundreds, 387 has 3 hundreds

Since 4 > 3, then 425 > 387

Step 2: Break down place values

425 = 400 + 20 + 5

387 = 300 + 80 + 7

Step 3: Final comparison

425 is greater than 387 because 4 hundreds > 3 hundreds

425 > 387
Final answer:

425 is greater than 387

Applied rules:

• Place value rule: Compare from highest place value to lowest

• Greater than: Use symbol > when first number is larger

• Less than: Use symbol < when first number is smaller

2 Equal Place Values
Exercise 2
Compare 543 and 572. Which number is greater?
Definition:

Equal hundreds: When hundreds are the same, compare tens place

Numbers
543 vs 572
Comparison
543 < 572
Step 1: Compare hundreds place

543 has 5 hundreds, 572 has 5 hundreds

Hundreds are equal, move to tens

Step 2: Compare tens place

543 has 4 tens, 572 has 7 tens

Since 4 < 7, then 543 < 572

Step 3: Final comparison

543 is less than 572 because 4 tens < 7 tens

543 < 572
Final answer:

543 is less than 572

Applied rules:

• Sequential comparison: Move to next place value when previous are equal

• Symbol usage: > for greater, < for less, = for equal

• Place value hierarchy: Hundreds > Tens > Ones

3 Same Hundreds and Tens
Exercise 3
Compare 634 and 639. Which number is greater?
Definition:

Same hundreds and tens: When hundreds and tens are equal, compare ones place

Numbers
634 vs 639
Comparison
634 < 639
Step 1: Compare hundreds place

634 has 6 hundreds, 639 has 6 hundreds

Hundreds are equal, move to tens

Step 2: Compare tens place

634 has 3 tens, 639 has 3 tens

Tens are equal, move to ones

Step 3: Compare ones place

634 has 4 ones, 639 has 9 ones

Since 4 < 9, then 634 < 639

Step 4: Final comparison

634 is less than 639 because 4 ones < 9 ones

634 < 639
Final answer:

634 is less than 639

Applied rules:

• Complete place value sequence: Hundreds → Tens → Ones

• Progressive comparison: Only move to next place when previous are equal

• Ones comparison: Final tie-breaker when hundreds and tens are equal

Rules and methods, laws,...
Hundreds > Tens > Ones
Place Value Hierarchy
Rule 1
Compare from LEFT to RIGHT
Start with highest place value
Rule 2
425 > 387
When hundreds differ
Rule 3
543 < 572
When hundreds equal, compare tens
Key definitions:

Greater than (>): First number is larger than second

Less than (<): First number is smaller than second

Equal (=): Both numbers have same value

Complete methodology:
  1. Identify place values: Separate hundreds, tens, and ones
  2. Compare from left: Start with hundreds place
  3. Move sequentially: Go to tens if hundreds equal, ones if tens equal
  4. Select symbol: Use >, <, or = appropriately
Tip 1: Always start comparing from the leftmost digit (highest place value).
Tip 2: If hundreds are the same, only then compare tens.
Tip 3: Write numbers vertically aligned to easily compare place values.
Tip 4: Remember: 425 > 399 even though 399 has higher tens and ones!
Common errors: Comparing from right to left, ignoring place value importance.
Memory aid: "H-T-O" (Hundreds, Tens, Ones) - always compare in this order.
Formulas to know by heart:

• Place value order: Hundreds > Tens > Ones

• Symbol meanings: > (greater than), < (less than), = (equal to)

• Comparison sequence: Left to right, highest to lowest place value

• Tie-breaking: Move to next place value when current are equal

• Visual alignment: Stack numbers to compare place values easily

Solution: Exercises 4 to 5
4 Ordering Multiple Numbers
Exercise 4
Order these numbers from least to greatest: 456, 398, 452, 501
Definition:

Ordering numbers: Arranging numbers from smallest to largest (ascending) or largest to smallest (descending)

Numbers
456, 398, 452, 501
Order
398, 452, 456, 501
Step 1: Compare hundreds place

398 has 3 hundreds (smallest)

456 and 452 both have 4 hundreds

501 has 5 hundreds (largest)

Step 2: Compare remaining numbers with 4 hundreds

456 vs 452: hundreds equal, compare tens

Both have 5 tens, compare ones: 6 > 2

So 452 < 456

Step 3: Arrange in order

398 (3 hundreds) < 452 (4 hundreds, 5 tens, 2 ones) < 456 (4 hundreds, 5 tens, 6 ones) < 501 (5 hundreds)

398 < 452 < 456 < 501
Final answer:

From least to greatest: 398, 452, 456, 501

Applied rules:

• Grouping by place value: Sort numbers by hundreds first

• Sequential comparison: Within groups, apply comparison rules

• Ascending order: Smallest to largest

5 Mixed Comparisons
Exercise 5
Fill in the blank with >, <, or =: 708 ___ 708
Definition:

Equality: Two numbers are equal when all place values are identical

Numbers
708 vs 708
Comparison
708 = 708
Step 1: Compare hundreds place

708 has 7 hundreds, 708 has 7 hundreds

Hundreds are equal, move to tens

Step 2: Compare tens place

708 has 0 tens, 708 has 0 tens

Tens are equal, move to ones

Step 3: Compare ones place

708 has 8 ones, 708 has 8 ones

All place values are equal

Step 4: Final conclusion

Since all place values match, 708 = 708

708 = 708
Final answer:

708 = 708

Applied rules:

• Equality rule: Numbers are equal when all place values match

• Reflexive property: Any number equals itself

• Systematic comparison: Check all place values systematically

Complete Guide to Comparing Numbers to 1000
Hundreds > Tens > Ones
Place Value System
Key definitions:

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

Comparison: Determining which number is greater, lesser, or equal

Ordering: Arranging numbers in ascending or descending sequence

Complete methodology:
  1. Identify place values: Separate hundreds, tens, and ones
  2. Compare from left: Start with highest place value (hundreds)
  3. Move sequentially: Go to tens if hundreds equal, ones if tens equal
  4. Select symbol: Use >, <, or = appropriately
  5. Verify: Double-check by reading numbers aloud
Tip 1: Always start comparing from the leftmost digit (highest place value).
Tip 2: If hundreds are the same, only then compare tens.
Tip 3: Write numbers vertically aligned to easily compare place values.
Tip 4: Remember: 425 > 399 even though 399 has higher tens and ones!
Tip 5: Use base-10 blocks or visual aids to understand place values.
Common errors: Comparing from right to left, ignoring place value importance, misreading zeros.
Memory aid: "H-T-O" (Hundreds, Tens, Ones) - always compare in this order.
Visual representation: Draw place value charts to organize comparisons.
Formulas to know by heart:

• Place value order: Hundreds > Tens > Ones

• Symbol meanings: > (greater than), < (less than), = (equal to)

• Comparison sequence: Left to right, highest to lowest place value

• Tie-breaking: Move to next place value when current are equal

• Visual alignment: Stack numbers to compare place values easily

• Ordering: Ascending (least to greatest) or descending (greatest to least)

Visual Comparison: Place Value Charts
Exercise 6: Understanding Place Values
Compare 842 and 837 using place value charts:
H | T | O
8 | 4 | 2
8 | 3 | 7

Analysis: The chart shows how place values determine number size.

  • Both numbers have 8 hundreds (equal)
  • Compare tens: 4 > 3, so 842 > 837
  • Ones place doesn't matter since tens differ

Questions & Answers

Question: I don't understand why 425 is bigger than 399. Doesn't 399 have bigger numbers in the tens and ones places?

Answer: Great question! This is a common confusion. The key is to understand that place value determines importance:

  • In 425: 4 hundreds = 400, 2 tens = 20, 5 ones = 5
  • In 399: 3 hundreds = 300, 9 tens = 90, 9 ones = 9

Even though 399 has more tens and ones, 425 has MORE hundreds. Since 400 > 300, the entire number 425 is greater than 399.

Think of it like money: $425 is more than $399 because you have more hundreds of dollars, even if the cents are smaller.

Always compare from left to right: hundreds first, then tens, then ones.

Question: My child gets confused when comparing numbers like 507 and 570. They think 507 is bigger because 7 is bigger than 5.

Answer: This is a classic mistake! Your child is focusing on individual digits rather than their place value. Here's how to help:

  • Write the numbers in expanded form: 507 = 500 + 0 + 7, 570 = 500 + 70 + 0
  • Use place value charts showing H|T|O columns
  • Point out that 570 has 7 tens (70) while 507 has 0 tens (0)

570 is greater because 7 tens (70) > 0 tens (0), even though 507 has a larger ones digit.

Use manipulatives like base-10 blocks to make the concept concrete: 570 has 5 hundreds blocks, 7 tens rods, and 0 units, while 507 has 5 hundreds, 0 tens, and 7 units.

Question: How do I quickly order many numbers like 234, 243, 324, 342?

Answer: Here's a systematic approach to ordering multiple numbers:

  1. Group by hundreds: 234 and 243 both have 2 hundreds, 324 and 342 both have 3 hundreds
  2. Within the 2-hundreds group: 234 vs 243 → compare tens: 3 < 4, so 234 < 243
  3. Within the 3-hundreds group: 324 vs 342 → compare tens: 2 < 4, so 324 < 342
  4. Combine groups: 234 < 243 < 324 < 342

The key is to work systematically: group by hundreds first, then order within each group.

You can also write them in a column format to visually align place values:

234

243

324

342

This makes it easier to compare digit by digit.