Writing Numbers in Expanded Form

Grade 2 Easy Number Sense & Place Value

Learning Objectives

  • Identify the tens and ones (and hundreds) places
  • Write numbers as the sum of their place values

Concept Explanation

Expanded form shows a number as the sum of the values of its digits. For instance, 123 can be written as 100 + 20 + 3. Recognizing place value (ones, tens, hundreds) ensures students accurately read, write, and compare numbers.

Worked Examples

Example 1

Problem: Write 45 in expanded form.
Solution: 40 + 5
Explanation: “4” is in the tens place (worth 40), “5” in the ones place (worth 5).

Example 2

Problem: Write 306 in expanded form.
Solution: 300 + 0 + 6
Explanation: There’s a zero in the tens place—still important to show.

Example 3

Problem: Which is larger in expanded form: 52 or 25?
Solution: 52 = 50 + 2; 25 = 20 + 5. 50 + 2 is bigger than 20 + 5.
Explanation: Compare place values rather than just digits.

Common Errors

ErrorCorrectionReason
Ignoring the 0 in the tens placeInclude every digit in expanded formEven if it’s 0, it holds a place (e.g., 407 = 400 + 0 + 7).
Writing digits out of orderIdentify digits from right (ones) to left (tens, hundreds)Misreading place values leads to incorrect expansions.
Mixing up tens and onesRecognize that the tens place is second from the rightConfusion can lead to 54 being written as 5 + 4 instead of 50 + 4.

Practice Problems

  1. Problem: Write 39 in expanded form.
    Solution: 30 + 9
  2. Problem: Which place is the digit 7 in 173?
    Solution: Tens place (70)
  3. Problem: Write 205 in expanded form.
    Solution: 200 + 0 + 5
  4. Problem: Is 60 + 4 the same as 24?
    Solution: No, 60 + 4 = 64.
  5. Problem: Identify the ones digit in 81.
    Solution: 1

Real-World Application Example

When reading house numbers, you might see 305. Knowing expanded form (300 + 0 + 5) helps you quickly recognize it’s three hundred and five, not thirty-five or another number.

Related Concepts