UPSC Prelims 2008 Q126: Science & Technology – Physics
How can the height of a person who is six feet tall be expressed (approximately) in
nanometres?
- (a) 183 × 10⁶ nanometres
- (b) 234 × 10⁶ nanometres
- (c) 183 × 10⁷ nanometres
- (d) 234 × 10⁷ nanometres
Answer: (c) 183 × 10⁷ nanometres
Explanation
Converting a person's height into nanometres
We need to express six feet in the extremely small unit of nanometres.
| Step | Calculation |
|---|---|
| Convert feet to metres | 6 feet ≈ 1.8288 metres |
| Convert metres to nanometres | 1 metre = 10⁹ nanometres |
| Calculate | 1.8288 × 10⁹ nm ≈ 1.83 × 10⁹ nm |
| Rewrite in the given format | 1.83 × 10⁹ = 183 × 10⁷ nanometres |
Why this conversion works:
| Point | Detail |
|---|---|
| 1 metre | 10⁹ nanometres |
| 6 feet | ≈1.83 metres |
Answer: (c) 183 × 10⁷ nanometres.
Why each option is right or wrong
- (a) Incorrect. 183 × 10⁶ understates the correct value by a factor of 10.
- (b) Incorrect. 234 × 10⁶ doesn't match the correct height conversion at all.
- (c) CORRECT. 1.83 metres × 10⁹ nm/metre = 183 × 10⁷ nanometres.
- (d) Incorrect. 234 × 10⁷ doesn't match the correct height conversion.
Key point
Six feet ≈ 1.83 metres; converting to nanometres (1 metre = 10⁹ nm) gives 1.83 × 10⁹ nm = 183 × 10⁷ nanometres.
Remember
Six feet ≈ 183 × 10⁷ nanometres.
Common mistakes
- Making a power-of-ten error while converting between metres and nanometres.
- Using an incorrect feet-to-metres conversion factor.
- Confusing the final answer's exponent notation (10⁶ vs 10⁷).
Exam tip
1 metre = 10⁹ nanometres. Always double-check the exponent when converting between vastly different unit scales.
Sources
- NCERT Class XI Physics — Units and Measurements
- Bureau International des Poids et Mesures (BIPM) — The International System of Units (SI Brochure), SI prefixes