Prefixes and Powers of Ten
An SI prefix denotes an exact factor 10^n attached to a unit symbol, and conversion requires compensating the numerical value so that the product of number and unit represents the same quantity.
Why this shows up in the exam
Choosing readable instrument ranges · Scientific notation in experiments · Comparing micro- and nanoscale devices
Learn the idea
SI prefixes scale a unit by an exact decimal power without changing the measured physical quantity. Changing kilometre to metre changes the numeral, not the road; prefixes move powers of ten between the number and the unit.
🧠 Memory hook: Move the prefix power into the number, with area and volume powers included.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- 1 km = 10³ m — kilo is an exact factor of one thousand
- 1 micro m = 10⁻⁶ m — micro is an exact factor of one millionth
- x u = (x 10ⁿ) U — conversion from a prefixed unit u to its unprefixed unit U
How to approach it
- 1Write the prefix as 10ⁿ
- 2Raise the factor if the unit is squared or cubed
- 3Check that the physical magnitude is unchanged
Common slip-ups that cost marks
- •Applying a length factor only once to area
- •Reversing milli and micro powers
- •Treating prefixes as measured uncertainties
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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