Expanded Form
Learn
Expanded form is a fun way to show what each digit in a number is really worth. It is like opening up a number to see inside!
What Is Expanded Form?
Expanded form shows a number as the sum of each digit's value. We "expand" the number to show what each part is worth.
For example: 347 = 300 + 40 + 7
Three Ways to Write Numbers
We can write the same number in three different ways:
- Standard form: 258 (the normal way)
- Expanded form: 200 + 50 + 8 (showing each value)
- Word form: two hundred fifty-eight (using words)
How to Write Expanded Form
Follow these steps:
- Find the value of the hundreds digit
- Find the value of the tens digit
- Find the value of the ones digit
- Write them with plus signs between them
What About Zeros?
When a digit is 0, we can skip it in expanded form:
- 405 = 400 + 5 (we skip the tens because there are 0 tens)
- 620 = 600 + 20 (we skip the ones because there are 0 ones)
Worked Examples
Example 1: Write 463 in expanded form
Problem: Write 463 in expanded form
Step 1: 4 is in the hundreds place = 400
Step 2: 6 is in the tens place = 60
Step 3: 3 is in the ones place = 3
Answer: 463 = 400 + 60 + 3
Example 2: Write 805 in expanded form
Problem: Write 805 in expanded form
Step 1: 8 is in the hundreds place = 800
Step 2: 0 is in the tens place = 0 (we skip this)
Step 3: 5 is in the ones place = 5
Answer: 805 = 800 + 5
Example 3: Write the standard form
Problem: What number is 500 + 30 + 7?
Step 1: 500 means 5 hundreds
Step 2: 30 means 3 tens
Step 3: 7 means 7 ones
Step 4: Put the digits together: 5, 3, 7
Answer: 500 + 30 + 7 = 537
Example 4: From expanded to standard form
Problem: What number is 200 + 9?
Step 1: 200 means 2 hundreds
Step 2: There is no tens part, so we have 0 tens
Step 3: 9 means 9 ones
Step 4: Put the digits together: 2, 0, 9
Answer: 200 + 9 = 209
Example 5: Write 940 in expanded form
Problem: Write 940 in expanded form
Step 1: 9 hundreds = 900
Step 2: 4 tens = 40
Step 3: 0 ones = 0 (we skip this)
Answer: 940 = 900 + 40
Practice Problems
Try these problems on your own. Click "Show Answer" to check your work!
Problem 1: Write 256 in expanded form.
Show Answer
200 + 50 + 6
Problem 2: Write 783 in expanded form.
Show Answer
700 + 80 + 3
Problem 3: What number is 400 + 20 + 1?
Show Answer
421
Problem 4: Write 609 in expanded form.
Show Answer
600 + 9 (we skip 0 tens)
Problem 5: What number is 300 + 70?
Show Answer
370
Problem 6: Write 842 in expanded form.
Show Answer
800 + 40 + 2
Problem 7: What number is 100 + 50 + 9?
Show Answer
159
Problem 8: Write 570 in expanded form.
Show Answer
500 + 70
Problem 9: What number is 900 + 4?
Show Answer
904
Problem 10: Write 111 in expanded form.
Show Answer
100 + 10 + 1
Check Your Understanding
Question 1: What is expanded form?
Show Answer
Expanded form shows a number as the sum of each digit's value, like 354 = 300 + 50 + 4.
Question 2: Why do we sometimes skip parts in expanded form?
Show Answer
We skip parts that equal zero. For example, in 402, we write 400 + 2 because there are no tens to include.
Question 3: What is 600 + 80 + 5 in standard form?
Show Answer
685
Question 4: How does expanded form help us understand numbers?
Show Answer
Expanded form helps us see the value of each digit. It shows that 456 is really 400 + 50 + 6, so we understand how big each part is!
Next Steps
- Practice: Write your address or phone number digits in expanded form
- Challenge: Try writing numbers in all three forms (standard, expanded, word)
- Connect: Use expanded form to help with addition problems
- Review: Go back to place value if you need more practice