Grade: Grade 2 Subject: Mathematics Unit: Place Value SAT: Algebra ACT: Math

Expanded Form

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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:

  1. Find the value of the hundreds digit
  2. Find the value of the tens digit
  3. Find the value of the ones digit
  4. 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