Place Value and Face Value — Definition and Difference

Face Value: • The digit itself, regardless of where it appears. • Face value of 6 is always 6, in any number.

Place Value: • The value of a digit based on its position. • Place value = face value × positional value

Example: Number = 5,472

Digit → Position → Face Value → Place Value 5 → Thousands → 5 → 5 × 1000 = 5000 4 → Hundreds → 4 → 4 × 100 = 400 7 → Tens → 7 → 7 × 10 = 70 2 → Ones → 2 → 2 × 1 = 2

Note: The face value of 0 is 0; the place value of 0 is also always 0.

Position → Place Value Ones → 1 Tens → 10 Hundreds → 100 Thousands → 1,000 Ten Thousands → 10,000 Lakhs → 1,00,000 Ten Lakhs → 10,00,000 Crores → 1,00,00,000

Example: Number = 73,45,812

Digit → Place → Place Value 7 → Ten Lakhs → 70,00,000 3 → Lakhs → 3,00,000 4 → Ten Thousands → 40,000 5 → Thousands → 5,000 8 → Hundreds → 800 1 → Tens → 10 2 → Ones → 2

Sum = 73,45,812 ✓

Face Value: • Fixed — does not change with position • Face value of 7 is always 7 • Used to identify the digit

Place Value: • Varies — depends on position in the number • The digit 7 has place value 7 in ones, 70 in tens, 700 in hundreds, etc. • Used to determine the actual contribution of a digit to the number

Special case — digit 0: • Face value = 0 (always) • Place value = 0 (always, regardless of position)

Relationship: Place Value = Face Value × Positional Value For the digit 6 in the hundreds place: Place Value = 6 × 100 = 600 Face Value = 6