SI prefixes from pico to tera, and converting very large or very small values
SI prefixes such as kilo (10³), milli (10⁻³) and micro (10⁻⁶) multiply a unit by a power of ten. Choose one that gives a number between 0.1 and 1000.
Why we need prefixes
Some values are huge. The mass of the Earth is about 5 970 000 000 000 000 000 000 000 kg. Some are tiny. The radius of a hydrogen atom is about 0.000 000 000 05 m. Long strings of zeros are hard to write and easy to get wrong. Scientific notation writes them with powers of ten: 5.97 × 10²⁴ kg and 5 × 10⁻¹¹ m. SI prefixes go one step further. A short word in front of the unit replaces the power of ten. So 5 × 10⁻¹¹ m becomes 50 pm (picometre).
SI prefixes from pico to tera
| Prefix | Symbol | Multiplies the unit by | Example |
|---|---|---|---|
| tera | T | 10¹² | 1 TW = 10¹² W |
| giga | G | 10⁹ | 2.4 GHz Wi-Fi signal |
| mega | M | 10⁶ | 93.5 MHz FM radio |
| kilo | k | 10³ | a 5 km run |
| hecto | h | 10² | 1013 hPa air pressure |
| deca | da | 10¹ | 1 dam = 10 m |
| deci | d | 10⁻¹ | 1 dm = 10 cm |
| centi | c | 10⁻² | a 30 cm ruler |
| milli | m | 10⁻³ | a 500 mg tablet |
| micro | μ | 10⁻⁶ | a red blood cell about 7 μm across |
| nano | n | 10⁻⁹ | a virus about 100 nm across |
| pico | p | 10⁻¹² | a hydrogen atom of radius 50 pm |
Rules for using prefixes
- Choose the prefix that puts the number between 0.1 and 1000: 6.96 × 10⁸ m = 696 Mm, or 0.696 Gm.
- Write no space between the prefix and the unit symbol: ng, not n g.
- Never use a prefix alone: write 10 μm or 10 μg, not 10 μ.
- Use only one prefix at a time: 10⁻¹² g is 1 pg, not 1 μμg.
- For mass, put the prefix on the gram, because the kilogram already has one: 10⁻⁶ kg = 1 mg, not 1 μkg.
- A power applies to the whole prefixed unit: 1 cm³ = (10⁻² m)³ = 10⁻⁶ m³, and 1 km² = 10⁶ m².
- Your NIOS lesson adds one more: do not use a prefix with °C. The current SI guide does allow it (m°C, a millidegree Celsius), but it is rare; give your lesson's rule if asked. The lesson's table also runs beyond this one, from yocto (10⁻²⁴) to yotta (10²⁴).
How to convert a value into a prefixed unit
- 1Write the value in scientific notation: 0.000 002 5 s = 2.5 × 10⁻⁶ s.
- 2Find the prefix with that power of ten: 10⁻⁶ is micro (μ).
- 3Replace the power with the prefix: 2.5 × 10⁻⁶ s = 2.5 μs.
- 4★Check that the number lies between 0.1 and 1000. If not, move three powers of ten and use the next prefix.
★ key step
Worked example: rewriting values with prefixes
Write each value with a suitable prefix: (a) 4.5 × 10⁻⁸ m (b) 2.4 × 10⁹ Hz (c) 0.000 75 kg (d) 1 500 000 W.
- (a) 4.5 × 10⁻⁸ m = 45 × 10⁻⁹ m = 45 nm.
- (b) 2.4 × 10⁹ Hz = 2.4 GHz.
- (c) 0.000 75 kg = 0.75 g (1 kg = 1000 g) = 750 mg.
- (d) 1 500 000 W = 1.5 × 10⁶ W = 1.5 MW.
45 nm; 2.4 GHz; 750 mg (or 0.75 g); 1.5 MW
Worked example: area with a prefix
A farm plot has an area of 0.02 km². How many square metres is this?
- 1 km = 10³ m, so 1 km² = (10³ m)² = 10⁶ m².
- 0.02 km² = 0.02 × 10⁶ m² = 2 × 10⁴ m².
- A common mistake is 0.02 × 1000 = 20 m², which forgets to square the prefix.
2 × 10⁴ m², that is 20 000 m²
Medicine strips say 500 mg or 650 mg, phone plans count data in GB, and FM stations are tuned in MHz. Reading the prefix right matters: 500 mg is half a gram, not half a kilogram.
1 marks: “What power of ten does the prefix 'nano' stand for?” 10⁻⁹.
2 marks: “Rewrite with a suitable SI prefix: (i) 3.2 × 10⁻⁷ m (ii) 7 × 10⁴ g.” (i) 3.2 × 10⁻⁷ m = 320 × 10⁻⁹ m = 320 nm. (ii) 7 × 10⁴ g = 70 × 10³ g = 70 kg.
2 marks: “Why is 1 km² not equal to 1000 m²?” The power applies to the whole prefixed unit: 1 km² = (1000 m)² = 1 000 000 m² = 10⁶ m².
Up by thousands: kilo, mega, giga, tera. Down by thousands: milli, micro, nano, pico.