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How do we use units, prefixes and scientific notation correctly in physics?

SI base and derived units, metric prefixes, scientific notation, significant figures and the consistent handling of units in calculations.

An SQA Advanced Higher Physics answer on units, prefixes and scientific notation, covering SI base and derived units, metric prefixes, writing and manipulating numbers in scientific notation, significant figures, and keeping units consistent in calculations.

Generated by Claude Opus 4.813 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this key area is asking
  2. SI base and derived units
  3. Metric prefixes
  4. Scientific notation and significant figures
  5. Examples in context
  6. Try this

What this key area is asking

The SQA wants you to use SI base and derived units, apply metric prefixes, write numbers in scientific notation, quote answers to an appropriate number of significant figures, and keep units consistent through a calculation. This skills strand underpins every calculation in the course and the project.

SI base and derived units

Every physical quantity has a unit traceable to the base units, and checking that the units on both sides of an equation match (dimensional consistency) is a quick way to catch errors. For example, energy in joules is kg m2s−2\text{kg m}^2\text{s}^{-2}, which you can confirm from Ek=12mv2E_k = \tfrac{1}{2}mv^2. Expressing a derived unit in base units is a common short question.

Metric prefixes

A frequent source of error is leaving a prefix in place during a calculation: 470 μF470\ \mu\text{F} must become 470×10−6 F470 \times 10^{-6}\ \text{F} before use. Mixing prefixed and base units in the same equation gives answers wrong by factors of a thousand or more. Converting everything to base SI units first is the safest habit.

Scientific notation and significant figures

Scientific notation makes very large and very small numbers (such as 1.6×10−19 C1.6 \times 10^{-19}\ \text{C}) easy to handle and reduces errors with strings of zeros. When multiplying and dividing, add or subtract the powers of ten and combine the leading numbers. Quoting too many significant figures implies a precision the data do not support; quoting too few throws away information. Match the least precise piece of data.

Examples in context

Astronomy routinely uses scientific notation for distances such as 9.5×1015 m9.5 \times 10^{15}\ \text{m} in a light year, where ordinary notation would be unwieldy. Electronics uses prefixes constantly, from microfarad capacitors to gigahertz processors, and a misread prefix can destroy a component. Laboratory work requires quoting results to the right number of significant figures so that the precision claimed matches the instruments used. Dimensional checks on a derived equation catch mistakes before any numbers are substituted.

Try this

Q1. Express the newton in SI base units. [1 mark]

  • Cue. kg m s−2\text{kg m s}^{-2} (from F=maF = ma).

Q2. Convert 2.2 nF2.2\ \text{nF} to farads in scientific notation. [1 mark]

  • Cue. 2.2×10−9 F2.2 \times 10^{-9}\ \text{F}.

Q3. State why prefixes must be converted to powers of ten before a calculation. [1 mark]

  • Cue. To keep units consistent; leaving a prefix gives an answer wrong by a power of ten.

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA AH style4 marksA capacitor has a capacitance of 4700 μF4700\ \mu\text{F} and is charged to 250 mV250\ \text{mV}. Express both quantities in scientific notation in SI base units, and calculate the charge stored.
Show worked answer →

Convert using the prefixes: μ\mu means ×10−6\times 10^{-6} and m\text{m} means ×10−3\times 10^{-3}.

Capacitance: 4700 μF=4.700×10−3 F4700\ \mu\text{F} = 4.700 \times 10^{-3}\ \text{F}.

Voltage: 250 mV=0.250 V=2.50×10−1 V250\ \text{mV} = 0.250\ \text{V} = 2.50 \times 10^{-1}\ \text{V}.

Charge: Q=CV=4.700×10−3×2.50×10−1=1.2×10−3 CQ = CV = 4.700 \times 10^{-3} \times 2.50 \times 10^{-1} = 1.2 \times 10^{-3}\ \text{C}.

Markers reward converting the prefixes to powers of ten, expressing both in scientific notation, and the charge with unit.

SQA AH style3 marksState the SI base units of force, and hence express the newton in base units.
Show worked answer →

Force is mass times acceleration, F=maF = ma.

Mass has the base unit kilogram (kg\text{kg}); acceleration has units metres per second squared (m s−2\text{m s}^{-2}).

So the newton in base units is kg m s−2\text{kg m s}^{-2}.

Markers reward starting from F=maF = ma, identifying the base units of mass and acceleration, and combining them to give kg m s−2\text{kg m s}^{-2}.

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