Place Value Up to Billions Worksheets for Grade 4 Students

Complete worksheets on identifying billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones place values with detailed solutions.

Place Value Chart Up to Billions
Billions
1,000,000,000
Hundred Millions
100,000,000
Ten Millions
10,000,000
Millions
1,000,000
Hundred Thousands
100,000
Ten Thousands
10,000
Thousands
1,000
Hundreds
100
Tens
10
Ones
1
1 Place value identification
Worksheet Exercise 1
In the number 2,345,678,901, what is the value of the digit 3? What is the value of the digit 8?
Definition:

Place value: The value of a digit based on its position in the number. Billions: The position representing 1,000,000,000 (1 followed by 9 zeros).

Method:
  1. Identify the position of the target digit
  2. Recognize the place value of that position
  3. Multiply the digit by the value of its position
Billions
2
Hundred Millions
3
Ten Millions
4
Millions
5
Hundred Thousands
6
Ten Thousands
7
Thousands
8
Hundreds
9
Tens
0
Ones
1
Step 1: Identify the position of digit 3

In 2,345,678,901, the digit 3 is in the hundred millions place

Step 2: Calculate the place value

Digit value = 3 × 100,000,000 = 300,000,000

Step 3: Identify the position of digit 8

In 2,345,678,901, the digit 8 is in the thousands place

Step 4: Calculate the place value

Digit value = 8 × 1,000 = 8,000

3 × 100,000,000 = 300,000,000
8 × 1,000 = 8,000
Final answer:

The value of the digit 3 is 300,000,000. The value of the digit 8 is 8,000.

Applied rules:

• Position recognition: Identify where the digit appears in the number

• Place value system: Billions (1,000,000,000), Hundred Millions (100,000,000), Ten Millions (10,000,000), Millions (1,000,000), Hundred Thousands (100,000), Ten Thousands (10,000), Thousands (1,000), Hundreds (100), Tens (10), Ones (1)

• Multiplication rule: Digit value = Digit × Place value

Tip: Count positions from right to left to find the position.
2 Expanded form activity
Worksheet Exercise 2
Write 5,678,901,234 in expanded form by showing the value of each digit.
Definition:

Expanded form: Writing a number as the sum of each digit multiplied by its place value.

Billions
5
Hundred Millions
6
Ten Millions
7
Millions
8
Hundred Thousands
9
Ten Thousands
0
Thousands
1
Hundreds
2
Tens
3
Ones
4
Step 1: Calculate each digit's value

Digit 5 (billions): 5 × 1,000,000,000 = 5,000,000,000

Digit 6 (hundred millions): 6 × 100,000,000 = 600,000,000

Digit 7 (ten millions): 7 × 10,000,000 = 70,000,000

Digit 8 (millions): 8 × 1,000,000 = 8,000,000

Digit 9 (hundred thousands): 9 × 100,000 = 900,000

Digit 0 (ten thousands): 0 × 10,000 = 0

Digit 1 (thousands): 1 × 1,000 = 1,000

Digit 2 (hundreds): 2 × 100 = 200

Digit 3 (tens): 3 × 10 = 30

Digit 4 (ones): 4 × 1 = 4

Step 2: Write in expanded form

5,678,901,234 = 5,000,000,000 + 600,000,000 + 70,000,000 + 8,000,000 + 900,000 + 0 + 1,000 + 200 + 30 + 4

5,000,000,000 + 600,000,000 + 70,000,000 + 8,000,000 + 900,000 + 1,000 + 200 + 30 + 4 = 5,678,901,234
Final answer:

5,678,901,234 in expanded form is: 5,000,000,000 + 600,000,000 + 70,000,000 + 8,000,000 + 900,000 + 1,000 + 200 + 30 + 4

Applied rules:

• Individual calculation: Calculate each digit's value separately

• Addition principle: Sum all individual values to get the original number

• Verification method: The sum should equal the original number

Place Value Concepts Up to Billions
Digit Value = Digit × Place Value
Basic Formula
Ones Place
× 1
Value = Digit × 1
Tens Place
× 10
Value = Digit × 10
Hundreds Place
× 100
Value = Digit × 100
Thousands Place
× 1,000
Value = Digit × 1,000
Ten Thousands Place
× 10,000
Value = Digit × 10,000
Hundred Thousands Place
× 100,000
Value = Digit × 100,000
Millions Place
× 1,000,000
Value = Digit × 1,000,000
Ten Millions Place
× 10,000,000
Value = Digit × 10,000,000
Hundred Millions Place
× 100,000,000
Value = Digit × 100,000,000
Billions Place
× 1,000,000,000
Value = Digit × 1,000,000,000
Key definitions:

Digit: Any symbol (0-9) used to make up a number

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

Number: A mathematical object used to count, measure, and label

Complete methodology:
  1. Locate the target digit: Find the specific digit in question
  2. Determine the position: Count positions from right to left (ones, tens, hundreds...)
  3. Recognize the place value: Know the value associated with each position
  4. Calculate the value: Multiply the digit by its place value
  5. Verify the answer: Ensure the calculated value makes logical sense
Tip 1: Always start counting positions from the rightmost digit (ones place).
Tip 2: Each position to the left is 10 times greater than the position to its right.
Tip 3: The same digit has different values in different positions (e.g., 5 in 500 vs 5 in 50).
Tip 4: Use commas to separate large numbers into groups of three for easier reading.
Common errors: Miscounting positions, confusing place names, forgetting to multiply by place value.
Memory aid: "O-H-T-T-T-H-M-T-H-B" - Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, Hundred Millions, Billions.
Place Value System:

• Rightmost position: Ones (1)

• Next position left: Tens (10)

• Next position left: Hundreds (100)

• Next position left: Thousands (1,000)

• Next position left: Ten Thousands (10,000)

• Next position left: Hundred Thousands (100,000)

• Next position left: Millions (1,000,000)

• Next position left: Ten Millions (10,000,000)

• Next position left: Hundred Millions (100,000,000)

• Next position left: Billions (1,000,000,000)

Decimal Comparison Rules:

• Left-to-right comparison: Compare digits from left to right

• Place value matters: A digit in higher place value is greater than any digit in lower place value

• Equal whole parts: When whole numbers are equal, compare decimal parts

Additional Place Value Exercises
3 Number comparison activity
Worksheet Exercise 3
Which is greater: 1,234,567,890 or 1,234,567,809? Explain your reasoning using place value.
Definition:

Number comparison: Determining which number is larger by comparing place values from left to right.

Billions
1
Hundred Millions
2
Ten Millions
3
Millions
4
Hundred Thousands
5
Ten Thousands
6
Thousands
7
Hundreds
8
Tens
9
Ones
0
Billions
1
Hundred Millions
2
Ten Millions
3
Millions
4
Hundred Thousands
5
Ten Thousands
6
Thousands
7
Hundreds
8
Tens
0
Ones
9
Step 1: Compare billions place

Both have 1 in billions place, so continue

Step 2: Compare hundred millions place

Both have 2 in hundred millions place, so continue

Step 3: Compare ten millions place

Both have 3 in ten millions place, so continue

Step 4: Compare millions place

Both have 4 in millions place, so continue

Step 5: Compare hundred thousands place

Both have 5 in hundred thousands place, so continue

Step 6: Compare ten thousands place

Both have 6 in ten thousands place, so continue

Step 7: Compare thousands place

Both have 7 in thousands place, so continue

Step 8: Compare hundreds place

Both have 8 in hundreds place, so continue

Step 9: Compare tens place

1,234,567,890 has 9 in tens place, 1,234,567,809 has 0 in tens place

Since 9 > 0, 1,234,567,890 > 1,234,567,809

1,234,567,890 > 1,234,567,809
Final answer:

1,234,567,890 is greater than 1,234,567,809 because in the tens place, 9 > 0.

Applied rules:

• Left-to-right comparison: Always compare from left to right

• Place value priority: Higher place values determine the comparison first

• Equal parts continue: When parts are equal, continue to the next place

4 Real-world application activity
Worksheet Exercise 4
A country has a population of 1,200,000,000 people. What is the value of the digit 2 in this number? How many more people does this country have compared to a country with 1,000,000,000 people?
Definition:

Real-world application: Using place value to solve practical problems involving large numbers.

Billions
1
Hundred Millions
2
Ten Millions
0
Millions
0
Hundred Thousands
0
Ten Thousands
0
Thousands
0
Hundreds
0
Tens
0
Ones
0
Step 1: Identify the position of digit 2

In 1,200,000,000, the digit 2 is in the hundred millions place

Step 2: Calculate the place value

Digit value = 2 × 100,000,000 = 200,000,000

Step 3: Calculate the difference

1,200,000,000 - 1,000,000,000 = 200,000,000

Step 4: Interpret the result

The first country has 200,000,000 more people than the second country.

2 × 100,000,000 = 200,000,000
1,200,000,000 - 1,000,000,000 = 200,000,000
Final answer:

The value of the digit 2 is 200,000,000. The country has 200,000,000 more people than the country with 1,000,000,000 people.

Applied rules:

• Practical application: Place value helps interpret large numbers in real contexts

• Population comparison: Subtracting large numbers requires place value understanding

• Real-world relevance: Place value is essential for interpreting statistics and data

5 Mixed operations activity
Worksheet Exercise 5
What is the total value of the billions digit and the ten millions digit in 3,456,789,012?
Definition:

Mixed operations: Combining place value identification with arithmetic operations.

Billions
3
Hundred Millions
4
Ten Millions
5
Millions
6
Hundred Thousands
7
Ten Thousands
8
Thousands
9
Hundreds
0
Tens
1
Ones
2
Step 1: Identify the billions digit

In 3,456,789,012, the billions digit is 3

Value of billions digit = 3 × 1,000,000,000 = 3,000,000,000

Step 2: Identify the ten millions digit

In 3,456,789,012, the ten millions digit is 5

Value of ten millions digit = 5 × 10,000,000 = 50,000,000

Step 3: Calculate the total value

Total value = 3,000,000,000 + 50,000,000 = 3,050,000,000

3,000,000,000 + 50,000,000 = 3,050,000,000
Final answer:

The total value of the billions digit and the ten millions digit in 3,456,789,012 is 3,050,000,000.

Applied rules:

• Digit identification: Locate specific digits in their respective places

• Value calculation: Determine the value of each digit separately

• Arithmetic combination: Add values to find totals

Place Value Up to Billions Summary
Comprehensive Learning Summary

Definitions and Key Concepts

Place Value: The value of a digit based on its position in a number. Each position represents a power of 10.

Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers.

Number: A mathematical object used to count, measure, and label.

Billion: The number 1,000,000,000 (1 followed by 9 zeros).

Core Rules and Principles

Place Value Rule: Digit Value = Digit × Place Value

Base-10 system: Each place value is 10 times the previous one.

Position matters: Same digit has different values in different positions.

Right-to-left counting: Positions increase from right to left.

Step-by-Step Methods

Place Value Identification:

  1. Locate the target digit in the number
  2. Count positions from right to left (ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions...)
  3. Identify the place value of that position
  4. Multiply the digit by its place value

Expanded Form:

  1. Identify the place value of each digit
  2. Calculate the value of each digit
  3. Express the number as the sum of these values
  4. Verify that the sum equals the original number

Examples (Simple to Advanced)

Simple Example: In 234, the value of 3 is 3 × 10 = 30.

Intermediate Example: In 5,678, the value of 6 is 6 × 1,000 = 6,000.

Advanced Example: In 3,456,789,012, the value of 4 is 4 × 100,000,000 = 400,000,000.

Tips and Memory Aids

Position counting: Start from the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions.

Each position is 10 times greater: Moving left increases the value by a factor of 10.

Commas help: Use commas to separate large numbers into groups of three for easier reading.

Common Mistakes to Avoid

Confusing positions: Mixing up millions, ten millions, and hundred millions positions.

Forgetting place values: Not multiplying by the correct place value.

Misreading large numbers: Losing track of position when working with billions.

Key Takeaways for Memorization

• The same digit has different values in different positions

• Each position to the left is 10 times greater than the position to its right

• Practice with large numbers builds confidence and accuracy

• Understanding place value is fundamental for all math operations

Digit Value = Digit × Place Value
Core Formula
Ones Place
× 1
Value = Digit × 1
Tens Place
× 10
Value = Digit × 10
Hundreds Place
× 100
Value = Digit × 100
Thousands Place
× 1,000
Value = Digit × 1,000
Ten Thousands Place
× 10,000
Value = Digit × 10,000
Hundred Thousands Place
× 100,000
Value = Digit × 100,000
Millions Place
× 1,000,000
Value = Digit × 1,000,000
Ten Millions Place
× 10,000,000
Value = Digit × 10,000,000
Hundred Millions Place
× 100,000,000
Value = Digit × 100,000,000
Billions Place
× 1,000,000,000
Value = Digit × 1,000,000,000
Key definitions:

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

Digit: Any of the symbols 0-9 used to make up a number

Number: A mathematical object used to count, measure, and label

Complete methodology:
  1. Identify the target digit: Locate the specific digit in question
  2. Determine the position: Count positions from right to left (ones, tens, hundreds...)
  3. Recognize the place value: Know the value associated with each position
  4. Calculate the value: Multiply the digit by its place value
  5. Verify the answer: Ensure the calculated value makes logical sense
Tip 1: Always start counting positions from the rightmost digit (ones place).
Tip 2: Each position to the left is 10 times greater than the position to its right.
Tip 3: The same digit has different values depending on its position (e.g., 5 in 500 vs 5 in 50).
Tip 4: Use commas to separate large numbers into groups of three for easier reading.
Common errors: Miscounting positions, confusing place names, forgetting to multiply by place value.
Memory aid: "O-H-T-T-T-H-M-T-H-B" - Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, Hundred Millions, Billions.
Place Value Rules:

• Base-10 system: Each place value is 10 times the previous one

• Position matters: Same digit has different values in different positions

• Right-to-left counting: Positions increase from right to left

• Zero as placeholder: Zeros hold place value positions

• Grouping convention: Commas separate every three digits starting from the right

Number Comparison Rules:

• Left-to-right comparison: Always compare from left to right

• Place value priority: Higher place values determine the comparison first

• Equal parts continue: When parts are equal, continue to the next place

Questions & Answers

Question: I don't understand why the same digit has different values in different positions. Why is the digit 5 in 5,000,000,000 worth 5,000,000,000 but the digit 5 in 500 worth only 500?

Answer: Great question! This happens because of the place value system. The value of a digit depends on its position in the number:

  • In 5,000,000,000: The 5 is in the billions place, so its value is 5 × 1,000,000,000 = 5,000,000,000
  • In 500: The 5 is in the hundreds place, so its value is 5 × 100 = 500
  • In 5: The 5 is in the ones place, so its value is 5 × 1 = 5

Think of it like money: a $5 bill is worth $5, but if you have 5 billion-dollar bills, that's worth $5,000,000,000. The digit "5" is the same, but where it sits (which "position") determines its total value. Each position to the left is worth 10 times more than the position to its right!

Examples:

  • 5 in 5: worth 5 × 1 = 5
  • 5 in 50: worth 5 × 10 = 50
  • 5 in 500: worth 5 × 100 = 500
  • 5 in 5,000: worth 5 × 1,000 = 5,000
  • 5 in 5,000,000,000: worth 5 × 1,000,000,000 = 5,000,000,000

Question: How do I know which position is which? I get confused about billions, hundred millions, ten millions, etc.

Answer: The key is to remember that you always start counting from the rightmost digit! Here's a helpful way to remember:

  • Rightmost digit: ONES place (position 1 from the right)
  • Second from right: TENS place (position 2 from the right)
  • Third from right: HUNDREDS place (position 3 from the right)
  • Fourth from right: THOUSANDS place (position 4 from the right)
  • Fifth from right: TEN THOUSANDS place (position 5 from the right)
  • Sixth from right: HUNDRED THOUSANDS place (position 6 from the right)
  • Seventh from right: MILLIONS place (position 7 from the right)
  • Eighth from right: TEN MILLIONS place (position 8 from the right)
  • Ninth from right: HUNDRED MILLIONS place (position 9 from the right)
  • Tenth from right: BILLIONS place (position 10 from the right)

Memory trick: Think "O-H-T-T-T-H-M-T-H-B" - Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, Hundred Millions, Billions. Each position has one more zero than the previous:

  • Ones = 1 (no zeros)
  • Tens = 10 (one zero)
  • Hundreds = 100 (two zeros)
  • Thousands = 1,000 (three zeros)
  • Ten thousands = 10,000 (four zeros)
  • Hundred thousands = 100,000 (five zeros)
  • Millions = 1,000,000 (six zeros)
  • Ten millions = 10,000,000 (seven zeros)
  • Hundred millions = 100,000,000 (eight zeros)
  • Billions = 1,000,000,000 (nine zeros)

For example, in 3,456,789,012:

  • 2 is in the ones place (value: 2 × 1 = 2)
  • 1 is in the tens place (value: 1 × 10 = 10)
  • 0 is in the hundreds place (value: 0 × 100 = 0)
  • 9 is in the thousands place (value: 9 × 1,000 = 9,000)
  • 8 is in the ten thousands place (value: 8 × 10,000 = 80,000)
  • 7 is in the hundred thousands place (value: 7 × 100,000 = 700,000)
  • 6 is in the millions place (value: 6 × 1,000,000 = 6,000,000)
  • 5 is in the ten millions place (value: 5 × 10,000,000 = 50,000,000)
  • 4 is in the hundred millions place (value: 4 × 100,000,000 = 400,000,000)
  • 3 is in the billions place (value: 3 × 1,000,000,000 = 3,000,000,000)

Question: What if there's a zero in the number? Does zero have a place value too?

Answer: Yes, zero does have a place value! Zero acts as a "placeholder" to show that a particular place value is empty. Even though zero itself is worth 0, it still holds an important position:

  • In 305: The 0 is in the tens place, so its value is 0 × 10 = 0
  • In 4,000: The 0s are in the hundreds, tens, and ones places, so their values are 0 × 100 = 0, 0 × 10 = 0, and 0 × 1 = 0
  • In 1,000,000,000: The 0s are in all places except the billions place, so their values are all 0

Without the zeros acting as placeholders, we couldn't tell the difference between:

  • 35 and 305
  • 4 and 4,000
  • 72 and 702
  • 1,000,000,000 and 1

So while zero's value is always 0 (because 0 × anything = 0), it plays a crucial role in showing us which place values are occupied by non-zero digits. The zeros keep all the other digits in their correct positions!

Example: In 5,060,708,009

  • 5 is in billions place: 5 × 1,000,000,000 = 5,000,000,000
  • 0 is in hundred millions place: 0 × 100,000,000 = 0
  • 6 is in ten millions place: 6 × 10,000,000 = 60,000,000
  • 0 is in millions place: 0 × 1,000,000 = 0
  • 7 is in hundred thousands place: 7 × 100,000 = 700,000
  • 0 is in ten thousands place: 0 × 10,000 = 0
  • 8 is in thousands place: 8 × 1,000 = 8,000
  • 0 is in hundreds place: 0 × 100 = 0
  • 0 is in tens place: 0 × 10 = 0
  • 9 is in ones place: 9 × 1 = 9