Understanding Place Value

Grade 2 Medium Number Sense & Place Value

Learning Objectives

  • Identify the place of digits in a number
  • Write numbers in expanded form to show the value of each digit

Concept Explanation

Place value tells us the position of a digit in a number, which determines its value. In 256, the digit 2 represents 200 (hundreds place), the 5 represents 50 (tens place), and the 6 represents 6 (ones place).

This concept is essential for reading and writing numbers correctly, as well as performing operations like addition, subtraction, multiplication, and division. A strong grasp of place value also makes it easier to understand larger numbers and decimals later on.

Worked Examples

Example 1

Problem: Write 123 in expanded form
Solution: 100 + 20 + 3
Explanation: The “1” is in the hundreds place (worth 100), “2” in the tens place (worth 20), and “3” in the ones place (worth 3).

Example 2

Problem: What is the value of “4” in 749?
Solution: 40
Explanation: The digit “4” is in the tens place, so it represents 40.

Example 3

Problem: Identify the digit in the hundreds place of 508
Solution: 5
Explanation: The “5” is in the hundreds place, representing 500.

Common Errors

ErrorCorrectionReason
Treating all digits equallyConsider each digit’s positionEach place has a different multiplier (ones, tens, hundreds).
Forgetting zero in expanded formInclude zero if it’s in tens or onesFor example, 305 should be 300 + 0 + 5, not just 300 + 5.
Mixing up the order of digitsIdentify from right to left (ones, tens, hundreds)Misplacing digits leads to incorrect expanded forms.

Practice Problems

  1. Problem: Write 45 in expanded form
    Solution: 40 + 5
  2. Problem: What is the value of the digit 3 in 538?
    Solution: 30 (tens place)
  3. Problem: Identify the digit in the ones place of 672
    Solution: 2
  4. Problem: Write 506 in expanded form
    Solution: 500 + 0 + 6
  5. Problem: Which digit is in the tens place of 940?
    Solution: 4

Real-World Application Example

Consider house numbers on a street. A house labeled 307 has a 3 in the hundreds place (300), a 0 in the tens place, and a 7 in the ones place. This makes it easier for mail carriers and drivers to identify the location correctly.

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