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Physics · Chapter 2: Physical Quantities and Measurement
SI Units and Prefixes
The International System of Units (SI), prefixes from pico to tera, converting units, and the rules for writing units correctly.
Key termRememberExampleWatch out
01Concept
Before 1960, different countries used different units: feet and pounds in Britain, maunds and seers in the subcontinent, metres in France. This caused confusion in trade and science. In 1960, scientists agreed on one system for the whole world: the Système International d'Unités, or SI.
Prefixes
Physics deals with very large and very small values. Instead of writing many zeros, we use prefixes. A prefix is a word or letter placed before a unit to show a multiple or a fraction of it. Each prefix stands for a power of ten.
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| tera | T | 10¹² | 1 TB hard disk = 10¹² bytes |
| giga | G | 10⁹ | 1 GHz = 10⁹ Hz |
| mega | M | 10⁶ | Tarbela produces thousands of MW |
| kilo | k | 10³ | 1 km = 1,000 m |
| centi | c | 10⁻² | 1 cm = 0.01 m |
| milli | m | 10⁻³ | 1 mm = 0.001 m |
| micro | µ | 10⁻⁶ | A human hair is about 70 µm thick |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m (size of molecules) |
| pico | p | 10⁻¹² | 1 pF = 10⁻¹² F |
Converting units
To convert, replace the prefix with its power of ten.
- 5 km = 5 × 10³ m = 5,000 m
- 250 mg = 250 × 10⁻³ g = 0.25 g
- 3.6 MW = 3.6 × 10⁶ W
- 72 km h⁻¹ = 72 × 1000 m ÷ 3600 s = 20 m s⁻¹
Rules for writing units
- Write the symbol, not a full stop after it: 5 kg, not 5 kg. or 5 Kg.
- Leave a space between the number and the unit: 20 m.
- Symbols are not made plural: 10 kg, not 10 kgs.
- Only one prefix at a time: 1 µg, not 1 mmg.
- A unit named after a person has a capital symbol (N, Pa, J) but a small first letter when written in full (newton).
02Real World Examples
Mobile data
Your 4G package of 10 GB means 10 × 10⁹ bytes. Phone storage of 128 GB uses the same prefix.
Medicine doses
A paracetamol tablet contains 500 mg = 0.5 g of the medicine. Getting the prefix wrong in a hospital could be deadly.
Power stations
Tarbela Dam can generate several thousand megawatts (MW); a ceiling fan uses about 75 W. The prefix shows the difference at once.
03Practice Questions
Try to answer in your own words first, then open the model answer.
Short questions
Q1.What is SI? Why was it needed?Show answer
Answer
SI (Système International) is the international system of units agreed in 1960 and used all over the world. It was needed because different countries used different units, which caused confusion in science and trade.
Q2.What is a prefix? Give the value of mega and micro.Show answer
Answer
A prefix is a word placed before a unit to show a power of ten.
- mega (M) = 10⁶
- micro (µ) = 10⁻⁶
Q3.Convert 4.5 km into metres and 350 mg into kilograms.Show answer
Answer
- 4.5 km = 4.5 × 10³ m = 4,500 m
- 350 mg = 350 × 10⁻³ g = 0.35 g = 0.35 × 10⁻³ kg = 3.5 × 10⁻⁴ kg
Q4.A car moves at 90 km h⁻¹. Find its speed in m s⁻¹.Show answer
Answer
- 90 km h⁻¹ = 90 × 1000 m ÷ 3600 s
- = 90,000 ÷ 3600
- = 25 m s⁻¹
Q5.Find the mistakes: "The mass is 5 Kgs."Show answer
Answer
- The symbol for kilogram is kg (small k), not Kg.
- Symbols are not made plural: write 5 kg, not 5 kgs.
Long questions
Q6.Write a note on SI prefixes. Give a table of six prefixes with symbols and values, and convert 0.0045 m into mm and µm.Show answer
Answer
| Prefix | Symbol | Value |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
- 0.0045 m = 4.5 × 10⁻³ m = 4.5 mm
- 0.0045 m = 4500 × 10⁻⁶ m = 4,500 µm