Introduction: What Is Grade 4 Place Value?

Have you ever looked at a number like 45,782 and wondered why the 4 is worth much more than the 2?

The answer is place value.

Place value tells us what each digit in a number is worth based on its position. For example, in 45,782, the digit 4 is in the ten-thousands place, so it represents 40,000. The digit 2 is in the ones place, so it represents 2.

Understanding grade 4 place value is important because it helps you read large numbers, write numbers in different forms, compare numbers, round numbers, and prepare for multi-digit operations.

You can learn this! Take one place at a time, look carefully at each digit, and practice explaining your thinking.

Quick Learning Map

What is place value?
Important vocabulary
The place-value chart
Reading and writing large numbers
Standard, word, and expanded forms
The value of a digit
Comparing multi-digit numbers
Ordering numbers
Rounding numbers
Step-by-step strategies
Visual models
Worked examples
Real-world applications
Common mistakes
Word problems
Practice exercises
Challenge problems
Quick quiz
Parent and teacher activities
Quick review

Common Core Alignment

4.NBT.A.1 — Recognize Place Value Relationships

Students recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

In simple language: each place is 10 times the value of the place immediately to its right. For example, 1,000 is 10 times 100. This article uses place-value charts and examples to make this relationship clear.

4.NBT.A.2 — Read and Write Multi-Digit Whole Numbers

Students read and write multi-digit whole numbers using standard numerals, number names, and expanded form.

Example: 63,405 = sixty-three thousand four hundred five = 60,000 + 3,000 + 400 + 5.

4.NBT.A.3 — Use Place Value to Round

Students use place value understanding to round multi-digit whole numbers to any place.

Example: 4,682 rounded to the nearest hundred is 4,700. This article teaches the reasoning behind the rounding decision.

Grade 4 Place Value Vocabulary

Term	Simple Definition	Example
Digit	One symbol used to write a number	7 is a digit
Place value	The value a digit has because of its position	7 in 700 is worth 700
Ones	The first place to the left of the decimal point	6 in 26
Tens	The place worth groups of ten	4 in 46
Hundreds	The place worth groups of one hundred	3 in 326
Thousands	The place worth groups of one thousand	5 in 5,000
Ten-thousands	Ten groups of 1,000	8 in 80,000
Hundred-thousands	One hundred groups of 1,000	2 in 200,000
Standard form	A number written using digits	45,621
Expanded form	A number written as a sum of place values	40,000 + 5,000 + 600 + 20 + 1
Word form	A number written using words	forty-five thousand…
Round	Find a nearby number that is easier to use	4,682 → 4,700

Core Concept 1: Understanding the Place-Value Chart

A Grade 4 student should be comfortable working with numbers through at least the millions.

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
1,000,000	100,000	10,000	1,000	100	10	1

Example: 583,241

Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
5	8	3	2	4	1

Therefore: 583,241 = 500,000 + 80,000 + 3,000 + 200 + 40 + 1.

Why Does Place Value Work?

Our number system is based on groups of 10. Each time we move one place to the left, the value becomes 10 times greater.

1 one = 1
1 ten = 10
1 hundred = 100
1 thousand = 1,000
1 ten-thousand = 10,000

For example: 10 × 100 = 1,000 and 10 × 1,000 = 10,000.

Core Concept 2: The Value of a Digit

A digit’s value depends on its position. In 77,777, the digit 7 appears five times, but each 7 has a different value.

Digit	Place	Value
7	Ten-thousands	70,000
7	Thousands	7,000
7	Hundreds	700
7	Tens	70
7	Ones	7

Example 1: What is the value of 6 in 46,291? Answer: 6,000.

Example 2: What is the value of 6 in 406,291? Answer: 6,000. The 4 is worth 400,000 because it is in the hundred-thousands place.

Core Concept 3: Reading Large Numbers

Commas help us separate numbers into groups. 425,738 is read as “four hundred twenty-five thousand seven hundred thirty-eight.”

2,405,016 is read as “two million four hundred five thousand sixteen.” The zero does not need to be spoken.

Core Concept 4: Standard, Word, and Expanded Form

Standard Form

The number is written using digits: 72,418.

Word Form

The number is written using words: seventy-two thousand four hundred eighteen.

Expanded Form

The number is broken into the value of each digit: 70,000 + 2,000 + 400 + 10 + 8.

Example: 305,624 = 300,000 + 5,000 + 600 + 20 + 4.

Core Concept 5: Zeros in Place Value

Zeros are important because they act as placeholders. In 405,207, the zeros show that there are 0 ten-thousands and 0 tens.

Expanded form: 400,000 + 5,000 + 200 + 7.

Core Concept 6: Comparing Numbers

When comparing numbers, start with the greatest place. Use > for greater than, < for less than, and = for equal to.

Example: 54,321 and 52,999. The ten-thousands digits are equal, but 4 > 2 in the thousands place, so 54,321 > 52,999.

Core Concept 7: Ordering Numbers

To order numbers from least to greatest, compare the greatest place first. If digits match, move one place to the right.

Example: 45,210, 42,999, 46,001, 45,201 → 42,999 < 45,201 < 45,210 < 46,001.

Core Concept 8: Rounding Numbers

Rounding finds a nearby number that is easier to use. Look at the digit immediately to the right of the place you are rounding.

0, 1, 2, 3, 4 → stay
5, 6, 7, 8, 9 → increase by 1

Example: 4,682 rounded to the nearest hundred is 4,700.

Step-by-Step Strategies

Strategy 1: Find the Value of a Digit

Locate the digit.
Identify its place.
Write the value of that place.
Multiply the digit by the place value.

Worked example: What is the value of 8 in 281,435? 8 is in the ten-thousands place. 8 × 10,000 = 80,000. Answer: 80,000.

Second example: In 63,712, the 3 is in the thousands place, so its value is 3,000.

Strategy 2: Write a Number in Expanded Form

Identify each digit.
Identify its place.
Find each digit’s value.
Add the values.

Example: 84,306 = 80,000 + 4,000 + 300 + 6.

Strategy 3: Compare Two Numbers

Start at the greatest place.
Compare the digits.
If they match, move right.
Stop when you find a difference.

Example: 73,425 and 73,215. The first different digit is in the hundreds place: 4 > 2. Therefore, 73,425 > 73,215.

Strategy 4: Round a Number

Find the place you’re rounding to.
Look one place to the right.
If that digit is 5 or greater, round up.
If it is 4 or less, keep the digit.
Change all digits to the right to zeros.

Example: 62,748 rounded to the nearest thousand is 63,000.

Visual Learning Suggestions

Visual Title	What Should Appear	Short Explanation
Grade 4 Place-Value Chart	Millions through Ones with digit columns	Students place digits in columns and identify values.
Place-Value Staircase	1 → 10 → 100 → 1,000 → 10,000 with ×10 arrows	Shows that moving left makes a value 10 times greater.
Number 583,241 Decomposed	583,241 → 500,000 + 80,000 + 3,000 + 200 + 40 + 1	Connects a number to expanded form.
Rounding Number Line	4,600 ← 4,682 → 4,700	Shows why 4,682 rounds to 4,700.

10 Worked Examples

Example 1

Question: What is the value of 5 in 35,214?

1: Find 5.

2: 5 is in the thousands place.

3: 5 × 1,000 = 5,000.

Answer: 5,000

Why it works: The position determines the value.

Example 2

Question: Write 46,203 in expanded form.

1: Find each nonzero digit.

2: 4 = 40,000; 6 = 6,000; 2 = 200.

3: 3 = 3.

Answer: 40,000 + 6,000 + 200 + 3

Why it works: Expanded form shows each place value.

Example 3

Question: Write 72,405 in word form.

1: Read the thousands group.

2: 72 thousand.

3: Read the ones group: 405.

Answer: seventy-two thousand four hundred five

Why it works: The comma separates periods.

Example 4

Question: What is the value of 9 in 394,721?

1: Find 9.

2: 9 is in the ten-thousands place.

3: 9 × 10,000 = 90,000.

Answer: 90,000

Why it works: Each place is ten times the one to its right.

Example 5

Question: Compare 85,426 and 85,624.

1: Compare ten-thousands and thousands.

2: 8 = 8; 5 = 5.

3: Hundreds: 4 < 6.

Answer: 85,426 < 85,624

Why it works: The first different digit decides.

Example 6

Question: Round 34,672 to the nearest thousand.

1: Find the thousands digit.

2: Thousands digit = 4.

3: Hundreds digit = 6, so round up.

Answer: 35,000

Why it works: The hundreds digit controls rounding to the thousand.

Example 7

Question: Order 18,450; 18,405; 19,001; 17,999.

1: Compare thousands groups.

2: 17,999 is smallest.

3: Then order the 18,000 numbers.

Answer: 17,999, 18,405, 18,450, 19,001

Why it works: Compare from the greatest place.

Example 8

Question: Find 300,000 + 40,000 + 2,000 + 500 + 8.

1: Combine place values.

2: 300,000 + 40,000 = 340,000.

3: Add 2,000 + 500 + 8.

Answer: 342,508

Why it works: Expanded form represents each place.

Example 9

Question: Round 695,481 to the nearest ten thousand.

1: Find the ten-thousands digit.

2: It is 9.

3: Thousands digit is 5, causing 9 to roll over.

Answer: 700,000

Why it works: Rounding can cause regrouping.

Example 10

Question: Find the number with 6 hundred-thousands, 3 thousands, 8 hundreds, and 4 ones.

1: Write each place value.

2: 600,000 + 3,000.

3: Add 800 + 4.

Answer: 603,804

Why it works: Zeros hold empty places.

Real-Life Applications

Shopping

A store sells $12,450 worth of products in one day. Place value helps identify ten-thousands, thousands, hundreds, tens, and ones.

Sports

A stadium has 54,600 seats. Students can identify the value of each digit or round the capacity.

School

A school district has 28,475 students. Rounding can give a quick estimate: 28,475 → 28,000 to the nearest thousand.

Games

A player earns 125,680 points. Place value helps compare that score with another player’s score.

Common Mistakes

Thinking a digit always has the same value

Incorrect thinking: “The 7 is worth 7.”

Why it is wrong: In 7,000, 7 is worth 7,000.

Correct approach: Always ask what place the digit is in.

Forgetting zeroes

Incorrect thinking: 405,207 becomes 45,27.

Why it is wrong: Zeroes hold places.

Correct approach: Keep every placeholder in the correct column.

Comparing from the ones place

Incorrect thinking: Comparing the last digits first.

Why it is wrong: The greatest place has the most information.

Correct approach: Start at the leftmost place.

Rounding the wrong digit

Incorrect thinking: Looking at the target digit instead of the digit to its right.

Why it is wrong: The next digit tells whether to round.

Correct approach: Find the target place, then look one place right.

Forgetting that 5 rounds up

Incorrect thinking: Keeping the digit when the next digit is 5.

Why it is wrong: 5–9 round up.

Correct approach: Use the 0–4 / 5–9 rule.

Misreading expanded form

Incorrect thinking: 45,28 instead of 45,208.

Why it is wrong: Place values must stay aligned.

Correct approach: Write each value in its correct column.

Problem-Solving Strategies for Word Problems

Understand the question.
Identify important information.
Choose the correct operation or place-value strategy.
Solve step by step.
Check that the answer makes sense.
Explain the answer in a complete sentence when appropriate.

Worked Word Problem 1

A library has 46,275 books. Another library has 43,891 books. Which has more? Compare the ten-thousands digits: both are 4. Compare thousands: 6 > 3. Therefore, 46,275 is greater.

Worked Word Problem 2

A school collected 58,462 cans. Round to the nearest thousand. The thousands digit is 8 and the hundreds digit is 4, so keep the 8. Answer: 58,000 cans.

Worked Word Problem 3

A stadium holds 72,500 people and 68,900 tickets are sold. 72,500 − 68,900 = 3,600, so 3,600 more tickets could be sold.

Practice Section

Level 1: Easy

What is the value of 4 in 34,215?

What is the value of 8 in 82,401?

Write 25,306 in expanded form.

and 61,405 in word form.

Write “forty-two thousand eight hundred seven” in standard form.

What place is the 9 in 93,214?

Write 500,000 + 20,000 + 300 + 6 in standard form.

Level 2: Practice

What is the value of 7 in 274,315?

Write 406,521 in expanded form.

Compare: 52,431 ___ 52,341.

Compare: 89,999 ___ 90,001.

Order from least to greatest: 45,201; 44,999; 45,210; 46,001.

Round 34,672 to the nearest thousand.

82,451 to the nearest hundred.

Round 165,432 to the nearest ten thousand.

Level 3: Challenge

What number is represented by 600,000 + 30,000 + 4,000 + 200 + 9?

Round 499,999 to the nearest thousand.

Which is greater: 305,902 or 350,209?

A number has 7 in the hundred-thousands place, 4 in the ten-thousands place, 2 in the thousands place, and 9 in the tens place. What is the number?

Write a number greater than 450,000 but less than 451,000 that has 6 in the hundreds place.

Find two different numbers that round to 50,000 when rounded to the nearest ten thousand.

Word Problems

A city has 324,650 residents. Round the population to the nearest thousand.

A school district has 48,275 students. What is the value of the 8?

A stadium has 76,500 seats. Another stadium has 69,850 seats. Which has more seats?

A company produced 405,620 toys. Write this number in expanded form.

A museum had 92,480 visitors last year. Round this number to the nearest ten thousand.

Mixed Review

Write 708,405 in word form.

What is the value of 7 in 572,631?

Compare 405,600 and 405,060.

Round 349,721 to the nearest thousand.

Write 800,000 + 60,000 + 4,000 + 300 + 20 + 1 in standard form.

Answer Key

Level 1

4,000
80,000
20,000 + 5,000 + 300 + 6
sixty-one thousand four hundred five
42,807
Ten-thousands place
520,306

2 – Level

70,000
400,000 + 6,000 + 500 + 20 + 1
52,431 > 52,341
89,999 < 90,001
44,999; 45,201; 45,210; 46,001
35,000
82,500
170,000

Level 3

634,209
500,000
350,209
742,090
Example: 450,600
Examples: 45,000 and 54,000. Both round to 50,000 to the nearest ten thousand.

Word Problems

325,000 — 324,650 rounds up because the hundreds digit is 6.
8,000 — the 8 is in the thousands place.
76,500-seat stadium — 76,500 > 69,850.
400,000 + 5,000 + 600 + 20.
90,000 — 92,480 rounds to 90,000 to the nearest ten thousand.

Mixed Review

seven hundred eight thousand four hundred five
70,000
405,600 > 405,060
350,000
864,321

Challenge Yourself

Challenge 1: Find More Than One Answer

Find three different numbers that are greater than 30,000, less than 31,000, and round to 30,000 to the nearest thousand. Possible answers: 30,100, 30,400, 30,499.

Challenge 2: Find the Error

A student says, “45,682 rounded to the nearest thousand is 45,000 because the hundreds digit is 6.” Is the student correct? No. The thousands digit is 5 and the hundreds digit is 6, so the answer is 46,000.

Challenge 3: Compare Strategies

Which is better for comparing 67,321 and 67,912: starting with the ones place or the greatest place? Starting with the greatest place is better because place-value comparison finds the first different digit from left to right.

Challenge 4: Create Your Own Number

Create a six-digit number with 5 in the hundred-thousands place, 2 in the thousands place, 7 in the tens place, and a value greater than 520,000. Example: 523,470.

Quick Quiz

What is the value of 6 in 64,231? A. 6 B. 60 C. 600 D. 60,000
Which is the expanded form of 35,204? A. 30,000 + 5,000 + 200 + 4 B. 3,000 + 500 + 20 + 4 C. 30,000 + 500 + 20 + 4 D. 35,000 + 204
Which number is greater? A. 42,315 B. 42,351 C. 41,999 D. 40,999
Round 56,721 to the nearest thousand. A. 56,000 B. 57,000 C. 56,700 D. 60,000
Which number has 8 in the ten-thousands place? A. 18,204 B. 81,204 C. 108,204 D. 8,120
Write 205,430 in expanded form.
Write seventy-four thousand six hundred nine in standard form.
What is the value of 3 in 438,521?
Round 274,600 to the nearest ten thousand.
A town has 83,450 residents. Another has 79,900. Which has more, and how many more?

Quiz Answer Key

D — 60,000
A — 30,000 + 5,000 + 200 + 4
B — 42,351
B — 57,000
A — 18,204
200,000 + 5,000 + 400 + 30
74,609
30,000
270,000
83,450 has more; 83,450 − 79,900 = 3,550.

Parent & Teacher Tips

Build numbers with digit cards and ask students to make the largest or smallest number.
Use real-world numbers such as prices, sports attendance, populations, and scores.
Play “Round It” by giving a number and a place to round to.
Create a human place-value chart with students holding digit cards.
Ask “How do you know?” so students explain their reasoning, not just the answer.

Frequently Asked Questions

What is place value in Grade 4 math?

Place value tells us how much a digit is worth based on its position in a number.

What are the place values in Grade 4?

Students commonly work with ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, and millions.

Why is place value important in Grade 4?

It supports reading, writing, comparing, rounding, and operations with multi-digit numbers.

What is expanded form?

Expanded form breaks a number into the values of its digits. For example, 54,321 = 50,000 + 4,000 + 300 + 20 + 1.

How do you compare two large numbers?

Start at the greatest place and compare digits from left to right until you find the first difference.

How do you round a number?

Find the place you are rounding to and look at the digit immediately to its right. A 5–9 rounds up; a 0–4 stays.

What is the difference between a digit and its value?

A digit is a symbol such as 7. Its value depends on its position; in 7,000, 7 has a value of 7,000.

Why are zeros important in place value?

Zeros act as placeholders and keep other digits in the correct positions.

Quick Review: What You Learned

A digit’s value depends on its position.
Each place to the left is 10 times greater than the place to its right.
Numbers can be written in standard, word, and expanded form.
Zeroes can act as important placeholders.
We compare large numbers starting at the greatest place.
We can order numbers from least to greatest or greatest to least.
We use place value when rounding numbers.
A number line can help us understand rounding.
Place value is useful in real-world situations involving money, populations, scores, and measurements.
Explaining why an answer works is an important part of mathematical thinking.

Final Practice Challenge

A city has 486,725 residents. Another city has 479,890 residents.

Which city has more residents?
What is the value of the digit 8 in 486,725?
Write 486,725 in expanded form.
Round 486,725 to the nearest thousand.
How many more residents does the larger city have?
Write a sentence explaining how place value helped you solve the problem.

Solution

486,725 is greater because the ten-thousands digit 8 is greater than 7.
The 8 is in the ten-thousands place, so its value is 80,000.
400,000 + 80,000 + 6,000 + 700 + 20 + 5.
487,000, because the hundreds digit is 7.
486,725 − 479,890 = 6,835.
Place value helped compare the numbers and round the larger number correctly.

Keep Practicing!

Place value becomes easier when you practice looking carefully at where each digit lives. When you see a large number, break it into places, identify each digit’s value, and work one step at a time.