Recipe

Convert between SI prefixes

Use when: a value is written with one prefix and you need it with another, or you need to compare two values with different prefixes

Goal: the same quantity written on the rung you need

Taught in Units, prefixes and scientific notation

1. 1

   Write down the prefix you have and the prefix you want, and where each sits on the ladder.

   Example

   From 4.7 kΩ to Ω: kilo is one rung above plain ohms.

   Why: the conversion only depends on how many rungs apart the two prefixes are.

2. 2

   Each rung is a factor of 1000. Count how many steps apart the two prefixes are.

   Example

   kilo to plain: one rung, so a factor of 1000.

   Why: every electronics prefix is 1000 times its neighbour, so rungs count factors of 1000.

3. 3

   Going to a smaller prefix makes the number bigger, so multiply. Going to a larger prefix makes it smaller, so divide.

   Example

   4.7 \times 1000 = 4700, so 4.7\ \text{k}\Omega = 4700\ \Omega.

   Why: smaller units need more of them to make the same amount.

4. 4

   A value written with a smaller prefix should have a bigger number in front.

   • 4700 Ω from 4.7 kΩ: smaller prefix, bigger number — done.
   • 0.0047 Ω from 4.7 kΩ: the number shrank while the prefix shrank — you divided instead of multiplied; redo it.

   Why: this one check catches the most common slip.