Understanding Place Value Concepts

Vocabulary

• Place Value: The worth of a digit determined by its position in a number. Example: In 4,523, the 4 in the thousands place equals 4,000.
• Value: The specific worth of a digit influenced by its place value. Example: The value of 4 in 4,523 is 4,000.
• Digit: A single numeral from 0 to 9, each having its own place value.
• Standard Form: Representation of numbers using digits. Example: 4,523.
• Expanded Form: A method of expressing numbers by detailing the value of each digit. Example: 4,523 = 4,000 + 500 + 20 + 3.
• Word Form: Expressing numbers in words. Example: 4,523 = "four thousand five hundred twenty-three."

Place Values

• Ones: The first position from the right. In 4,523, the digit 3 represents 3.
• Tens: The second position from the right. In 4,523, the digit 2 represents 20.
• Hundreds: The third position from the right. In 4,523, the digit 5 represents 500.
• Thousands: The fourth position from the right. In 4,523, the digit 4 represents 4,000.

Place Value Chart

• Thousands: 4
• Hundreds: 5
• Tens: 2
• Ones: 3

Number Forms

• Standard Form: 4,523
• Expanded Form: 4,000 + 500 + 20 + 3
• Word Form: Four Thousand Five Hundred Twenty-Three

Example Problems

• Identify Place Value:

  • In 6,432, the value of 6 is 6,000 (thousands place).
  • In 3,781, the value of 8 is 80 (tens place).

• Write in Expanded Form:

  • 369 in expanded form is 300 + 60 + 9.
  • 7,204 in expanded form is 7,000 + 200 + 4.

• Write in Word Form:

  • 52 in word form is Fifty-two.
  • 9,107 in word form is Nine thousand one hundred seven.

• Comparing Numbers:

  • Between 4,523 and 4,752, 4,752 is greater due to the higher hundreds place (7 vs. 5).
  • Between 3,204 and 3,240, 3,204 is smaller as its tens place (0) is less than that of 3,240 (4).