Definition of Face Value

  • Face value is the actual value of a digit in a number.
  • It remains the same regardless of the digit’s position.
  • For example, in 327, the face value of 3 is 3.
  • In 4,504, the face value of 0 is 0.
  • Face value is always a single-digit number.

Definition of Place Value

  • Place value is the value of a digit depending on its position in a number.
  • It is calculated as: Place value = Face value × Positional value
  • Example: In 3,427, the place value of 4 is 400.
  • In 6,012, the place value of 1 is 10.

Key Differences

  • Face value does not change with position; place value depends on position.
  • Face value of 7 in 7,000 = 7; Place value = 7000.
  • Face value is the digit itself; place value is the digit multiplied by its base power.
  • Face value is always less than or equal to the place value.

Indian Place Value System

  • Digit positions: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Crores.
  • Example: In 58,72,145 —
    • Place value of 5 = 50,00,000
    • Face value of 5 = 5

International Place Value System

  • Digit positions: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions.
  • This system is used in science, commerce, and international banking.

Examples for Practice

  • In 5,843:
    • Face value of 8 = 8
    • Place value of 8 = 800
  • In 92,407:
    • Face value of 9 = 9
    • Place value of 9 = 90,000
  • In 70,321:
    • Face value of 0 = 0
    • Place value of 0 = 0

Use in Number Expansion

  • Place value is used in expanded form of numbers.
  • Example: 5,082 = 5,000 + 80 + 2
  • Face value helps identify each digit's contribution to total value.

Importance in Exams

  • Commonly tested in topics under number system.
  • Appears in SSC, RRB, Banking, and state-level exams.
  • Also useful in data interpretation, estimation, and rounding off.

Decimal Place Values

  • Digits after the decimal have place values like:
    • First digit = tenths (1/10)
    • Second digit = hundredths (1/100)
    • Third digit = thousandths (1/1000)
  • In 23.475, place value of 7 = 0.07, face value = 7

Miscellaneous Facts

  • Place value increases 10 times as you move left in a number.
  • Every digit in a number has a unique face value and a unique place value.
  • The digit 0 always has zero face value and zero place value.
  • Understanding place value is essential for learning about large numbers, decimals, and algebra.

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