Definition

  • Place value is the value a digit holds based on its position in a number.
  • Face value is the value of the digit itself, regardless of its position.
  • In other words, place value = face value × positional value.

Basic Concepts

  • The face value of a digit is always the digit itself. (e.g., face value of 7 is 7)
  • The place value depends on the position of the digit in the number.
  • For example, in the number 5,783, the place value of 7 is 700.
  • In the same number, the face value of 7 is just 7.

Indian Place Value System

  • Follows the pattern: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores
  • Example: In 74,53,218:
    • Place value of 7 = 70,00,000
    • Place value of 4 = 4,00,000

International Place Value System

  • Follows the pattern: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions
  • Used in global contexts such as finance, science, and business.

Important Place Values

  • Unit (ones) place: 1×digit
  • Tens place: 10×digit
  • Hundreds place: 100×digit
  • Thousands place: 1,000×digit
  • Ten thousand place: 10,000×digit
  • Lakhs and crores follow higher multiples in the Indian system.

Examples

  • In 3,624, place value of 6 = 600, face value = 6
  • In 58,102, place value of 1 = 100, face value = 1
  • In 1,00,002, place value of 1 = 1,00,000

Key Differences

  • Face value is constant, but place value varies depending on the digit’s position.
  • Example: In 242, the digit 2 appears twice:
    • First 2 (Hundreds) has place value 200
    • Second 2 (Units) has place value 2
    • Both have face value = 2

Uses in Exams and Arithmetic

  • Frequently asked in number system questions in SSC, RRB, Banking exams.
  • Useful in understanding expanded forms of numbers.
  • Helps in solving rounding-off, comparison, and estimation problems.
  • Important for learning decimal places and fractions too.

Decimal Place Values

  • After the decimal point: tenths (1/10), hundredths (1/100), thousandths (1/1000), etc.
  • In 12.345, place value of 3 = 0.3, 4 = 0.04, 5 = 0.005

Expanded Form

  • Helps to break down numbers based on their place values.
  • Example: 4,362 = 4,000 + 300 + 60 + 2
  • Face values used to assign place-based values in writing numbers in expanded form.

Miscellaneous Facts

  • Face value of 0 is always 0, and its place value is also 0.
  • The highest place value in a number depends on its number of digits.
  • Digits closer to the left have higher place values.
  • This concept builds the base for understanding number systems and mathematics operations.

Category

Questions