Units, prefixes and standard form
SI units and prefixes
Every physics equation works when you put the numbers in SI units: metres, kilograms, seconds, amps, and the units built from them (newtons, joules, watts, volts, ohms).
A prefix in front of a unit is just a power of ten.
| Prefix | Symbol | Multiply by |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| milli | m | 10⁻³ |
| micro | μ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
- A resistor is 4.7 kΩ. In ohms?
- k means × 10³
- 4.7 × 10³ Ω = 4700 Ω
Going the other way you divide: 0.045 A is 0.045 ÷ 10⁻³ = 45 mA. If the number got bigger when the unit got bigger, you went the wrong way.
Standard form
Standard form writes a number as A × 10ⁿ, with A from 1 up to (but not including) 10.
Big numbers have a positive power, numbers smaller than 1 a negative one.
- Light travels at 300 000 000 m/s
- Point after the first digit: 3.0, and it moved 8 places
- 300 000 000 = 3.0 × 10⁸ m/s
- A hair is 0.000 075 m thick: 7.5 × 10⁻⁵ m
When you multiply, multiply the numbers in front and add the powers. When you divide, divide the numbers and subtract the powers.
- Charge of 2.5 × 10¹⁸ electrons, each 1.6 × 10⁻¹⁹ C
- 2.5 × 1.6 = 4.0, and 18 + (−19) = −1
- 4.0 × 10⁻¹ C = 0.40 C
Units before numbers: a 2.0 kW heater for 3 minutes is 2000 W × 180 s, not 2.0 × 3. Convert every prefix and every minute first.
Standard form on the calculator
Use the ×10ˣ key, never "× 10 ^". A power station gives out 1.2 × 10⁹ W for one hour. Type 1.2, press ×10ˣ, type 9, then × 3600 and =. You should get 4.32 × 10¹² J. Now try 3.0 × 10⁸ ÷ 5.0 × 10⁻⁷ typed with ×10ˣ both times: the frequency of green light, 6 × 10¹⁴ Hz. What do you get if you type the second number without the ×10ˣ key, as × 10 ^ −7? Why is it wrong?
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