METRIC CONVERSION :
Introduction
Understanding metric conversion is a fundamental skill in CBSE Physics for Classes IX and XI, as it allows you to express physical quantities ranging from the vast (distance between stars in kilometers) to the minute (wavelength of light in nanometers) using a consistent system of prefixes and powers of ten.
The metric system, or SI (Système International d’Unités), is built on base units like the meter, kilogram, and second, and uses prefixes such as kilo (10³), centi (10⁻²), milli (10⁻³), and micro (10⁻⁶) to scale these units up or down without changing their nature. Every numerical problem in kinematics, dynamics, or thermodynamics—whether converting 5 km to meters or 250 mg to kilograms—requires you to multiply or divide by the correct power of ten.
Mastering this process ensures your final answers are not off by factors of 10, 100, or 1,000, a common source of marks deduction in CBSE exams. Once you internalize the simple rule—moving the decimal point left when converting to a larger unit and right when converting to a smaller unit—metric conversion becomes a quick, reliable step that strengthens all your subsequent physics calculations.
PREFIXES AND POWERS OF TEN :
Why Metric Conversion Matters in CBSE Physics
In Class IX and XI, you often need to convert:
- cm → m (length)
- g → kg (mass)
- ms → s (time)
- μm → m (microphysics)
- km → m (distance in kinematics)
Common CBSE Exam Mistakes (and Fixes)
| Mistake | Fix |
|---|---|
| Confusing milli (10⁻³) and micro (10⁻⁶) | Write powers explicitly: 1 mA = 10⁻³ A, 1 μA = 10⁻⁶ A |
| Adding instead of multiplying prefixes | Use conversion factor chain: |
| Wrong decimal shift | Count zeros in the prefix difference. |
| Forgetting that 1 cm² = (10⁻² m)² = 10⁻⁴ m² |
Apply power to both number and unit. |
Practice Problems (with answers hidden)
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Convert 0.05 m to mm.
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A wire is 2.5 km long. Express in cm.
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1 microsecond = ? seconds (in scientific notation)
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250 cm³ = ? m³
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Speed = 72 km/h. Convert to m/s.
(Answers: 50 mm, 250,000 cm, 1×10⁻⁶ s, 2.5×10⁻⁴ m³, 20 m/s)Metric Conversion Quiz – CBSE Class IX / XI
Q1. Convert 2.5 kilometers into meters.
A) 25 m
B) 250 m
C) 2500 m
D) 25,000 m✅ Correct Answer: C) 2500 m
Explanation: 1 km = 1000 m, so 2.5 × 1000 = 2500 m.
Q2. Which of the following is equal to 1 milligram?
A) 10⁻³ g
B) 10⁻⁶ kg
C) 10⁻³ kg
D) Both A and B✅ Correct Answer: D) Both A and B
Explanation: 1 mg = 10⁻³ g = 10⁻⁶ kg. Option C (10⁻³ kg) would be 1 gram, which is incorrect.
Q3. A wire is 0.05 meters long. What is its length in centimeters?
A) 0.5 cm
B) 5 cm
C) 50 cm
D) 500 cm✅ Correct Answer: B) 5 cm
Explanation: 1 m = 100 cm, so 0.05 × 100 = 5 cm.
Q4. Convert 72 km/h to m/s.
*(Hint: 1 km = 1000 m, 1 h = 3600 s)*A) 20 m/s
B) 25.9 m/s
C) 72 m/s
D) 7.2 m/s✅ Correct Answer: A) 20 m/s
Explanation: m/s.
Q5. A capacitor has a capacitance of 2.5 microfarads (μF). Express this in farads (F) using scientific notation.
A) 2.5 × 10⁻⁹ F
B) 2.5 × 10⁻⁶ F
C) 2.5 × 10⁻³ F
D) 2.5 × 10⁶ F✅ Correct Answer: B) 2.5 × 10⁻⁶ F
Explanation: micro (μ) = 10⁻⁶, so 2.5 μF = 2.5 × 10⁻⁶ F.
📝 Quick Quiz: Metric Conversion
- Convert 2.5 km to m.
A) 25 m B) 250 m C) 2500 m D) 25000 m
✅ Answer: C - 1 milligram = ?
A) 10⁻³ g B) 10⁻⁶ kg C) 10⁻³ kg D) A and B
✅ Answer: D - 0.05 m = ? cm
A) 0.5 cm B) 5 cm C) 50 cm D) 500 cm
✅ Answer: B - 72 km/h = ? m/s
A) 20 m/s B) 25.9 m/s C) 72 m/s D) 7.2 m/s
✅ Answer: A - 2.5 μF = ? F
A) 2.5×10⁻⁹ F B) 2.5×10⁻⁶ F C) 2.5×10⁻³ F D) 2.5×10⁶ F
✅ Answer: B
Check your answers above. Each wrong answer? Review the prefixes table!
📏 Metric Conversion Quiz – Answer Sheet
⏱️ Metric Conversion Quiz
CBSE Class IX / XI | 5 questions | 01:00 remaining
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