Prefixes, intervals and units
Use the prefix factor with the original unit. A conversion preserves the quantity, while its numerical value changes
- pico (p) Multiply the unprefixed unit by this factor \(\displaystyle 10^{-12}\)
- nano (n) Multiply the unprefixed unit by this factor \(\displaystyle 10^{-9}\)
- micro (µ) Multiply the unprefixed unit by this factor \(\displaystyle 10^{-6}\)
- milli (m) Multiply the unprefixed unit by this factor \(\displaystyle 10^{-3}\)
- centi (c) Multiply the unprefixed unit by this factor \(\displaystyle 10^{-2}\)
- deci (d) Multiply the unprefixed unit by this factor \(\displaystyle 10^{-1}\)
- deca (da) Multiply the unprefixed unit by this factor \(\displaystyle 10^{1}\)
- hecto (h) Multiply the unprefixed unit by this factor \(\displaystyle 10^{2}\)
- kilo (k) Multiply the unprefixed unit by this factor \(\displaystyle 10^{3}\)
- mega (M) Multiply the unprefixed unit by this factor \(\displaystyle 10^{6}\)
- giga (G) Multiply the unprefixed unit by this factor \(\displaystyle 10^{9}\)
- tera (T) Multiply the unprefixed unit by this factor \(\displaystyle 10^{12}\)
Worked example
Two instrument readings are 2.3 × 10⁻⁶ s and 7.8 × 10⁻⁶ s from the same origin. Find the elapsed time in microseconds
\[\begin{aligned}t_1&=2.3\times10^{-6}\text{ s}\\t_2&=7.8\times10^{-6}\text{ s}\end{aligned}\]
- \(\displaystyle 7.8-2.3=5.5\)Subtract the earlier time from the later time
- \(\displaystyle \Delta t=5.5\times10^{-6}\text{ s}\)Both readings use the same power of ten
- \(\displaystyle 5.5\times10^{-6}\text{ s}=5.5\,\mathrm{\mu s}\)Micro means 10⁻⁶
Common mistakes
Reversing the prefix sign
✕\(\displaystyle 1\text{ ng}=10^9\text{ g}\)✓\(\displaystyle 1\text{ ng}=10^{-9}\text{ g}\)
Nano means one billionth of the unprefixed unitAdding the times
✕\(\displaystyle 7.8+2.3=10.1\)✓\(\displaystyle 7.8-2.3=5.5\)
An elapsed time is a difference, not the sum of timestampsDifficulty levels
introConvert milli-, centi- and kilo- masses to an ordinary numeral in grams
standardConvert each prefix from pico through tera to scientific notation in grams
challengeFind short or geological time intervals, or compare durations by division
examConvert between prefixed units in either direction
Questions about this topic
Does a smaller unit give a larger numerical count?+
Yes. The same quantity contains more of a smaller unit. For example, 1 µs contains 1,000 ns
Are prefixes such as mega and milli interchangeable?+
No. Prefix symbols are case-sensitive; M means mega and m means milli
Do bytes always use powers of 1,000?+
Decimal SI prefixes do: a kilobyte is 1,000 bytes. Binary prefixes such as kibi are a different system
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 6: Indices and surds
In this chapter
Work with index notationExpress a number in prime-factor index formSimplify using index laws 1 and 2Simplify using index law 3 and the zero powerExpand using index laws 4 and 5Work with negative indicesSolve an exponential equation by matching basesCombine positive and negative integer indicesScientific notationMultiply and divide in scientific notationSI prefixes and scientific timescalesRound to decimal places and significant figuresRecord measurements and compare instrumentsRelate fractional indices to roots (optional extension)Locate exact square roots on the real number lineSimplify, compare and operate with surds (optional practice)