Understanding Place Value Answer Key for 3rd Grade Students

Complete answer key with detailed solutions, visual aids, and step-by-step guidance for place value exercises.

Answer Key: Exercises 1 to 3
1 Place Value Identification
Exercise 1
What is the value of the digit 7 in 573?
Definition:

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

Digit Position: Each position has a specific value (ones, tens, hundreds)

Place Value Identification Method:
  1. Identify the position of the target digit
  2. Determine the place value name (ones, tens, hundreds)
  3. Calculate the actual value (digit × place value)
Answer Key:

In 573:

5 is in the hundreds place (5 × 100 = 500)

7 is in the tens place (7 × 10 = 70)

3 is in the ones place (3 × 1 = 3)

Therefore, the value of the digit 7 is 70.

H
T
O
5
7
3
500
70
3
The value of digit 7 in 573 is 70
Final answer:

The value of the digit 7 in 573 is 70.

Applied rules:

• Position Value: The tens place is worth 10 times the digit

• Digit Multiplication: Multiply the digit by its place value

• Value Recognition: 7 in the tens place = 7 × 10 = 70

2 Expanded Form
Exercise 2
Write 428 in expanded form.
Definition:

Expanded Form: Writing a number as the sum of each digit's place value

Place Value Expression: Showing how each digit contributes to the total

Expanded Form Method:
  1. Identify each digit and its place value
  2. Express each digit as its value (digit × place value)
  3. Connect with addition signs
Answer Key:

In 428:

4 is in the hundreds place: 4 × 100 = 400

2 is in the tens place: 2 × 10 = 20

8 is in the ones place: 8 × 1 = 8

Expanded form: 400 + 20 + 8

H
T
O
4
2
8
400
20
8
428 = 400 + 20 + 8
Final answer:

428 in expanded form is 400 + 20 + 8.

Applied rules:

• Place Value Multiplication: Each digit is multiplied by its place value

• Sum Expression: Expanded form shows the sum of place values

• Digit Position: Position determines the multiplier (1, 10, 100)

3 Number Comparison
Exercise 3
Which is greater: 347 or 374? Explain your answer using place value.
Definition:

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

Place Value Comparison: Comparing numbers by examining each place value from left to right

Number Comparison Method:
  1. Compare digits in the highest place value first
  2. If digits are equal, move to the next lower place value
  3. Continue until a difference is found
  4. Determine which number is greater based on the comparison
Answer Key:

Comparing 347 and 374:

Hundreds place: 3 vs 3 (equal, move to tens)

Tens place: 4 vs 7 (4 < 7, so 347 < 374)

Therefore, 374 is greater than 347.

H
T
O
3
4
7
3
7
4
vs
vs
vs
374 > 347
Final answer:

374 is greater than 347 because in the tens place, 7 > 4.

Applied rules:

• Left-to-Right Comparison: Start with the highest place value

• Place Value Hierarchy: Higher place values determine the comparison

• Sequential Evaluation: Move to lower places only when upper places are equal

Place Value Concepts and Rules
473 = 4×100 + 7×10 + 3×1
Place Value Formula
Place Value
H T O
Hundreds, Tens, Ones
Range
0-9
Digits in each place
Multiplier
×100, ×10, ×1
For H, T, O
Key definitions:

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

Expanded Form: Writing a number as the sum of each digit's place value

Standard Form: The usual way of writing numbers (e.g., 473)

Place Value Analysis:
  1. Digit Recognition: Identify each digit in the number
  2. Position Assignment: Assign hundreds, tens, or ones position
  3. Value Calculation: Multiply digit by its place value (100, 10, 1)
  4. Number Composition: Express as sum of place values
  5. Comparison: Compare using place value hierarchy
Tip 1: Always read numbers from left to right (hundreds, tens, ones).
Tip 2: The hundreds place is worth 100 times the digit, tens worth 10 times, ones worth 1 time.
Tip 3: When comparing, start with the largest place value first.
Tip 4: Expanded form shows exactly how each digit contributes to the total value.
Answer Key: Exercises 4 to 5
4 Place Value Puzzles
Exercise 4
I am a three-digit number. My tens digit is 5. My hundreds digit is 2 more than my ones digit. My ones digit is 3. What number am I?
Definition:

Place Value Puzzles: Word problems requiring analysis of digit relationships

Digit Relationships: Connections between digits in different places

Answer Key:

Given information:

- Tens digit = 5

- Ones digit = 3

- Hundreds digit = ones digit + 2 = 3 + 2 = 5

Therefore, the number is 553.

Step 1: Identify known digits

Tens digit = 5, Ones digit = 3

Step 2: Calculate the hundreds digit

Hundreds digit = ones digit + 2 = 3 + 2 = 5

Step 3: Assemble the number

Hundreds = 5, Tens = 5, Ones = 3

The number is 553

H
T
O
5
5
3
The number is 553
Final answer:

The number is 553.

Applied rules:

• Systematic Analysis: Work through each clue methodically

• Relationship Recognition: Identify how digits relate to each other

• Step-by-Step Solution: Solve one piece at a time

5 Word Problem with Place Value
Exercise 5
A school has 427 students. Another school has 472 students. Which school has more students? How many more?
Definition:

Word Problems: Real-life scenarios requiring mathematical operations

Place Value Application: Using place value concepts in practical contexts

Answer Key:

Comparing 427 and 472:

Hundreds place: 4 vs 4 (equal)

Tens place: 2 vs 7 (2 < 7)

Therefore, 472 > 427

Difference: 472 - 427 = 45

The second school has 45 more students.

Step 1: Compare the numbers using place value

427 vs 472

Hundreds: 4 = 4 (move to tens)

Tens: 2 < 7, so 427 < 472

Step 2: Calculate the difference

472 - 427 = 45

Step 3: State the complete answer

The second school (472 students) has more students.

It has 45 more students than the first school.

H
T
O
4
2
7
4
7
2
Second school has more students (472 > 427), 45 more than the first
Final answer:

The second school has more students. It has 45 more students than the first school.

Applied rules:

• Problem Analysis: Identify numbers and what's being asked

• Place Value Comparison: Use place value to determine greater number

• Difference Calculation: Find how much more one number is than another

Complete Summary: Understanding Place Value
473 = 400 + 70 + 3 = 4×100 + 7×10 + 3×1
Place Value Representation
Key definitions:

Place Value: Each digit has a value based on its position in a number

Expanded Form: Expressing a number as the sum of each digit's place value

Standard Form: The typical way of writing numbers

Complete methodology:
  1. Digit Recognition: Identify each digit in the number
  2. Position Assignment: Assign hundreds, tens, or ones position
  3. Value Calculation: Multiply each digit by its place value (100, 10, 1)
  4. Number Expression: Write as sum of place values
  5. Comparison: Compare using place value hierarchy
  6. Application: Use in word problems and puzzles
Tip 1: The leftmost digit represents hundreds (multiply by 100).
Tip 2: The middle digit represents tens (multiply by 10).
Tip 3: The rightmost digit represents ones (multiply by 1).
Tip 4: When comparing, start with the largest place value first.
Common errors: Confusing place values, forgetting to multiply by place value, starting comparisons from the wrong direction.
Key concepts: Each place is 10 times the value of the place to its right.
Place Value Rules:

• Position Value: Hundreds place = digit × 100, Tens place = digit × 10, Ones place = digit × 1

• Comparison: Compare from left to right (highest place value first)

• Expanded Form: Write as sum of each digit's place value

• Base Ten System: Each place is 10 times the value of the place to its right

• Digit Range: Each place can hold digits 0-9

Place Value Answer Key Summary
Exercise Solutions Overview
Quick reference for all place value exercises
Exercise Problem Type Key Concept Answer
1 Place Value Identification Digit Value 7 in 573 = 70
2 Expanded Form Place Value Expression 428 = 400+20+8
3 Number Comparison Place Value Hierarchy 374 > 347
4 Place Value Puzzle Digit Relationships 553
5 Word Problem Real-World Application 472 > 427 by 45

Scoring Guide: Each exercise typically worth 5 points (1 for setup, 2 for process, 2 for correct answer).

Common Mistakes: Forgetting place value multipliers, reversing comparison symbols, misreading digits.

Questions & Answers

Question: My child keeps confusing the value of digits in different places. How can I help them understand that the same digit has different values?

Answer: This is a very common challenge! Try these strategies:

  • Concrete Materials: Use base ten blocks to show 1 hundred block vs 1 ten rod vs 1 unit cube
  • Money Connection: Relate to dollars ($100), dimes ($10), and pennies ($1)
  • Place Value Charts: Write numbers in columns to visually separate positions
  • Verbal Reinforcement: Always say "four hundreds" not just "four" when reading 473
  • Practice Games: Play games where they identify digit values in random numbers

The key is connecting the abstract symbol to its concrete value through multiple representations.

Question: Why do we need to learn expanded form? It seems like extra work.

Answer: Expanded form is actually very helpful because it:

  • Builds Understanding: Shows exactly how each digit contributes to the total
  • Prevents Errors: Helps avoid mistakes in addition and subtraction
  • Prepares for Advanced Math: Essential for understanding decimals and larger numbers
  • Improves Mental Math: Makes it easier to add and subtract mentally
  • Shows Number Relationships: Reveals the structure of our number system

Think of it like taking apart a toy to see how it works - expanded form shows how numbers are built!

Question: When comparing numbers, why do we start from the left side instead of the right?

Answer: We start from the left because the leftmost digits have the greatest value:

  • Highest Impact: The hundreds place is worth much more than tens or ones
  • Efficiency: Often we can decide which number is bigger by just looking at the first digit
  • Logical Order: It's like comparing the biggest parts first, then the smaller parts
  • Consistency: This method works for any number of digits

For example, 300 is much bigger than 299, even though 299 has larger digits in the tens and ones places.