Identify the Value of the Underlined Digit: Complete Worksheet Guide

Master the skill of identifying the value of underlined digits with this comprehensive tutorial covering definitions, examples, methods, and practice problems.

Identify the Value of the Underlined Digit
1 Basic digit value identification
Example 1
Find the value of the underlined digit in 5432.
Definition:

Digit value: The actual value of a digit based on its position in a number. Calculated as digit × place value.

Method for finding digit value:
  1. Locate the underlined digit in the number
  2. Identify the place value of that position
  3. Multiply the digit by its place value
Thousands
5
Hundreds
4
Tens
3
Ones
2
Number
5,432
Underlined Digit
5
Value
5 × 1000
Step 1: Identify the position

The underlined 5 is in the thousands place

Step 2: Determine the place value

The thousands place has a value of 1,000

Step 3: Calculate the digit value

Value = digit × place value = 5 × 1,000 = 5,000

5,432 = 5,000 + 400 + 30 + 2
Final answer:

The value of the underlined 5 in 5,432 is 5,000.

Applied rules:

• Place value: Each position has a specific value (ones, tens, hundreds, thousands)

• Multiplication: Digit value = digit × place value

• Position matters: The same digit in different positions has different values

Tip: Count positions from the right to identify place values quickly.
Mistake to avoid: Don't forget to multiply by place value, just stating the digit isn't the value.
2 Different position digit value
Example 2
Find the value of the underlined digit in 7248.
Definition:

Same digit, different value: The same digit in different positions has different values.

Thousands
7
Hundreds
2
Tens
4
Ones
8
Number
7,248
Underlined Digit
2
Value
2 × 100
Step 1: Locate the underlined digit

The underlined 2 is in the hundreds place

Step 2: Identify the place value

The hundreds place has a value of 100

Step 3: Calculate the value

Value = digit × place value = 2 × 100 = 200

7,248 = 7,000 + 200 + 40 + 8
Final answer:

The value of the underlined 2 in 7,248 is 200.

Applied rules:

• Position matters: The same digit (2) has different values in different positions

• Place value system: Each position has a specific value

• Multiplication: Always multiply digit by place value

3 Tens place digit value
Example 3
Find the value of the underlined digit in 9,573.
Definition:

Tens place: The second position from the right, with a place value of 10.

Thousands
9
Hundreds
5
Tens
7
Ones
3
Number
9,573
Underlined Digit
7
Value
7 × 10
Step 1: Identify the position

The underlined 7 is in the tens place

Step 2: Determine the place value

The tens place has a value of 10

Step 3: Calculate the digit value

Value = digit × place value = 7 × 10 = 70

9,573 = 9,000 + 500 + 70 + 3
Final answer:

The value of the underlined 7 in 9,573 is 70.

Applied rules:

• Tens place value: Always 10 regardless of the digit

• Multiplication: Digit value = digit × 10

• Position identification: Count from the right to determine position

Place Value System & Digit Value Rules
Digit\ Value = Digit × Place\ Value
Digit Value Formula
Ones Place
1
Value = digit × 1
Tens Place
10
Value = digit × 10
Hundreds Place
100
Value = digit × 100
Thousands Place
1000
Value = digit × 1000
Key definitions:

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

Digit value: The actual value of a digit, calculated as digit × place value

Underlined digit: A digit specifically highlighted for value calculation

Position: The location of a digit in a number, starting from the right

Place value identification method:
  1. Start from the right: Ones, tens, hundreds, thousands...
  2. Count positions: Each position is 10 times larger than the one before
  3. Identify underlined digit: Locate the specific digit to evaluate
  4. Determine place value: Based on the digit's position
  5. Calculate value: Multiply digit by its place value
Tip 1: Use commas to separate periods (thousands, millions) to identify place values easily.
Tip 2: Each place value is 10 times the previous one (1, 10, 100, 1000...).
Tip 3: Count positions from the right to identify the place value of any digit.
Advanced Digit Value Concepts
4 Large number digit value
Example 4
Find the value of the underlined digit in 45,678.
Definition:

Large numbers: Same process but with more positions (ten thousands, hundred thousands...).

Ten Thousands
4
Thousands
5
Hundreds
6
Tens
7
Ones
8
Number
45,678
Underlined Digit
4
Value
4 × 10000
Step 1: Identify the position

The underlined 4 is in the ten thousands place

Step 2: Determine the place value

The ten thousands place has a value of 10,000

Step 3: Calculate the digit value

Value = digit × place value = 4 × 10,000 = 40,000

45,678 = 40,000 + 5,000 + 600 + 70 + 8
Final answer:

The value of the underlined 4 in 45,678 is 40,000.

Applied rules:

• Large numbers: Same process regardless of size

• Higher positions: Greater place values (ten thousands, hundred thousands, millions...)

• Consistent method: Always multiply digit by its place value

5 Zero digit value
Example 5
Find the value of the underlined digit in 7084.
Definition:

Zero digits: Even if a digit is zero, it still represents a place value position.

Thousands
7
Hundreds
0
Tens
8
Ones
4
Number
7,084
Underlined Digit
0
Value
0 × 100
Step 1: Identify the position

The underlined 0 is in the hundreds place

Step 2: Determine the place value

The hundreds place has a value of 100

Step 3: Calculate the digit value

Value = digit × place value = 0 × 100 = 0

7,084 = 7,000 + 0 + 80 + 4
Final answer:

The value of the underlined 0 in 7,084 is 0.

Applied rules:

• Zero rule: Any digit 0 multiplied by any place value equals 0

• Place value preservation: Zeros still occupy positions in the number

• Position importance: The place value system still applies to zeros

Digit Value Applications & Patterns
abcde = (a×10000) + (b×1000) + (c×100) + (d×10) + (e×1)
Digit Value Formula
Key definitions:

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

Digit value: The actual value of a digit, calculated as digit × place value

Underlined digit: A digit specifically highlighted for value calculation

Position: The location of a digit in a number, starting from the right

Complete methodology:
  1. Locate underlined digit: Identify the specific digit to evaluate
  2. Determine position: Count from the right to find the place value
  3. Identify place value: Each position has a specific value (ones, tens, hundreds, thousands...)
  4. Calculate value: Multiply the digit by its place value
  5. State the answer: Express the value clearly
Tip 1: Use commas to separate periods and help identify place values quickly.
Tip 2: Count positions from right to left to identify the place value of any digit.
Tip 3: Remember that each position is 10 times the value of the position to its right.
Tip 4: Even zeros have place values, though their digit value is always 0.

Common errors: Confusing digit value with place value, miscounting positions, forgetting to multiply by place value.
Exam preparation: Practice with various number sizes, pay attention to zeros, memorize place value names.
Place values to know:

• Ones: 1

• Tens: 10

• Hundreds: 100

• Thousands: 1,000

• Ten Thousands: 10,000

• Each place value is 10 times the previous one

Comprehensive Summary: How to Identify the Value of Underlined Digit
Key Concepts & Definitions:

Place Value: The value of a digit based on its position in a number. Each position is 10 times larger than the position to its right.

Digit Value: The actual value of a digit, calculated as digit × place value. Example: In 543, the digit value of 5 is 5 × 100 = 500.

Underlined Digit: A digit specifically highlighted for value calculation purposes.

Position: The location of a digit in a number, counting from the right (ones, tens, hundreds, thousands...).

Standard Form: The normal way of writing numbers. Example: 543

Period: A group of three digits separated by commas. Example: 543,789 (543 in the thousands period, 789 in the ones period)

Core Rules & Principles:

• Place Value Progression: Each position increases by a factor of 10 moving left: ..., 1,000,000, 100,000, 10,000, 1,000, 100, 10, 1, 0.1, 0.01, 0.001, ...

• Multiplication Rule: Each digit must be multiplied by its corresponding place value

• Zero Handling: Zeros still represent their place value even though the product equals zero

• Position Counting: Always count from the right to identify place values

Step-by-Step Methods:
  1. Locate the Underlined Digit: Identify the specific digit to evaluate in the given number
  2. Determine the Position: Count from the right to find which place value position the digit occupies
  3. Identify the Place Value: Determine the specific value for that position (ones = 1, tens = 10, hundreds = 100, etc.)
  4. Calculate the Digit Value: Multiply the digit by its place value
  5. State the Answer: Clearly express the calculated value
Examples (Simple → Advanced):

Simple: In 543, the underlined 5 is in hundreds place: 5 × 100 = 500

Intermediate: In 7248, the underlined 2 is in hundreds place: 2 × 100 = 200

Advanced: In 45,678, the underlined 4 is in ten thousands place: 4 × 10,000 = 40,000

With Zeros: In 7084, the underlined 0 is in hundreds place: 0 × 100 = 0

Ones Place: In 5432, the underlined 2 is in ones place: 2 × 1 = 2

Tips: Use commas to separate periods, count positions from right to left, remember each position is 10 times the one to its right.
Common Pitfalls: Confusing digit value with place value, miscounting positions, forgetting to multiply by place value.
Key Takeaways: Place value is fundamental to understanding all arithmetic operations. Practice regularly with increasingly complex numbers. Verification by addition ensures accuracy.

Questions & Answers

Question: I don't understand why we need to learn this. Why can't we just write numbers normally?

Answer: Great question! Understanding digit values helps you in many important ways:

  • Builds number sense: It shows you that 5,432 really means 5 thousands, 4 hundreds, 3 tens, and 2 ones
  • Prepares for operations: Understanding place value makes addition, subtraction, multiplication, and division much easier
  • Works with decimals later: The same concept applies to decimal numbers
  • Real-world applications: Understanding large numbers like population counts, money amounts, and measurements

Think of it like learning the alphabet before reading - understanding digit values teaches you how numbers are built from smaller parts!

Example: When you add 5,432 + 1,234, knowing that 5,432 = 5,000 + 400 + 30 + 2 helps you add the thousands to thousands, hundreds to hundreds, etc.

Question: What happens when there's a zero in the middle of a number? Does it still have a value?

Answer: Yes, zeros still have place values, but their digit value is always 0:

  • Still represents place: In 7,080, the zero is in the hundreds place
  • Value calculation: (0 × 100) = 0
  • Important for structure: The zero holds the place value position in the number

Example: In 7080, the underlined 0 is in the hundreds place, so its value is 0 × 100 = 0.

Even though the value is 0, the zero is still important because without it, the number would be 780 instead of 7,080!

Tip: Always include zeros in your place value analysis - they maintain the number's structure.

Question: My child is struggling with place value concepts. How can I help them practice at home?

Answer: Here are effective ways to support your child's learning:

  • Use manipulatives: Base-10 blocks or play money to physically represent place values
  • Make it visual: Draw place value charts with columns for each position
  • Practice with real numbers: Prices, ages, distances - make it relevant
  • Play games: "What's the value of this digit?" with random numbers

Daily practice examples:

• Look at license plates, house numbers, or prices and practice identifying digit values

• Start with smaller numbers and gradually increase difficulty

• Encourage your child to read numbers aloud before identifying digit values

Remember: Patience and repetition are key. Celebrate small victories to build confidence!