Percentage uncertainty questions
Work with absolute and percentage uncertainty, repeated readings and timing.
Units, prefixes and standard form
Practise SI prefix conversions, standard form, squared and cubed units, and units in calculations.
Practise
Cubed unitsA sample has a volume of 9.2 m³. Express it in mm³.
Hint
One m³ is (103)^3 = 109 mm³. Apply the prefix conversion to every length factor.
Worked solution
- 1 m³ = (103)^3 = 109 mm³.
- 9.2 m³ = 9.2 × 109 mm³ = 9.2 × 109 mm³.
Question type: Mixed practice
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Converting units
A prefix multiplies a unit by a power of ten. For example, 1 mA = 10⁻³ A, so 3.2 mA = 0.0032 A. In the other direction, 0.0032 A = 3.2 mA.
For area, square the length conversion: 1 cm² = (10⁻² m)² = 10⁻⁴ m². For volume, cube it: 1 cm³ = (10⁻² m)³ = 10⁻⁶ m³.
SI prefixes
| Prefix | Symbol | Factor |
|---|---|---|
| femto | f | 10-15 |
| pico | p | 10-12 |
| nano | n | 10-9 |
| micro | μ | 10-6 |
| milli | m | 10-3 |
| centi | c | 10-2 |
| deci | d | 10-1 |
| kilo | k | 103 |
| mega | M | 106 |
| giga | G | 109 |
| tera | T | 1012 |
Standard form and answers
In standard form, a number is written as a × 10ⁿ, where 1 ≤ a < 10 for positive values. For example, 0.00042 = 4.2 × 10⁻⁴.
Conversions here are exact: do not round them. Current questions ask for 3 significant figures; a more precise answer is accepted if it rounds to the same value. Trailing zeros need not be typed. This is a practice marking rule, not an exam-board marking scheme.
Femto is included for AQA; deci is included for OCR A. The resource practises prefixes and standard form, with area and volume conversions. It does not cover all base/derived units or energy-unit conversions.
A-level relevance
AQA 7408: 3.1.1 (partial); OCR A H556: 2.1.2(e) (partial). Tasks cover the selected skills listed above.