03. Place Value & Face Value

Place Value aur Face Value ka clear concept: definition, difference, base-10 positions, expanded form, digits value, common traps, SSC CGL level examples & practice questions with answers.

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1) Face Value (Simple)

Face value ka matlab: digit jo dikh raha hai, uski original value. Isme position matter nahi karti.

• Example: number 507 me digit 5 ka face value = 5
• Example: number 9090 me digit 9 ka face value = 9 (dono jagah same)

2) Place Value (Concept)

Place value digit ki value hoti hai jo uski position par depend karti hai. Base-10 (decimal system) me har left shift par value 10 times ho jati hai.

Base-10 positions (right to left)

• Ones = 10⁰
• Tens = 10¹
• Hundreds = 10²
• Thousands = 10³
• Ten-thousands = 10⁴ … and so on

Formula (Most Useful)

Place value = digit × 10^k where k = right side se position count (ones ke liye k=0).

3) Place Value vs Face Value (Difference)

4) Expanded Form (SSC favourite)

Kisi bhi number ko place values ke sum me likhna expanded form hota hai.

• 507 = 5×100 + 0×10 + 7×1 = 500 + 0 + 7
• 9042 = 9×1000 + 0×100 + 4×10 + 2×1

5) Decimal numbers me place value

Decimal point ke right side par places negative powers hoti hain:

• Tenths = 10⁻¹
• Hundredths = 10⁻²
• Thousandths = 10⁻³

• Example: 12.345 me 3 ka place value = 3×10⁻¹ = 0.3
• 12.345 me 4 ka place value = 0.04
• 12.345 me 5 ka place value = 0.005

6) Important SSC-type Examples

Example 1

Number: 72864. Digit 2 ka face value aur place value?

• Face value = 2
• 2 tens-thousands place par hai ⇒ place value = 2×10⁴ = 20000

Example 2

Number: 5608. Digit 6 ka place value?

• 6 hundreds place par ⇒ 6×100 = 600

Example 3 (Decimal)

Number: 0.072. Digit 7

• 7 hundredths place par ⇒ 7×10⁻² = 0.07

7) Common Traps (Exam me dhyan)

• Same digit ki face value same hoti hai, but place value different ho sakti hai. Example: 9090 me 9 ka place value 9000 aur 90 dono ho sakta hai.
• Decimal me right side tenths/hundredths confuse mat karo.
• Zero digit ka place value always 0 hota, but position identify karna still important (expanded form).

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8) Practice Questions (with Answers)

1. Number 48372 me digit 8 ka face value aur place value?
2. Number 9005 me digit 9 ka place value?
3. 12.406 me digit 4 ka place value?
4. 0.509 me digit 9 ka place value?
5. Number 70070 me digit 7 ke dono occurrences ki place value likho.
6. Expanded form likho: 3409

Show Answers

1. Face value 8; place value 8000 (thousands place)
2. 9000
3. 4×10⁻¹ = 0.4
4. 9×10⁻³ = 0.009
5. 70000 and 70
6. 3409 = 3×1000 + 4×100 + 0×10 + 9×1