Appropriate Units in Calculations Revision Notes for AQA A-Level Biology

Appropriate Units in Calculations

Using correct units is essential in biological calculations. Units must always be clearly written and consistently applied throughout your working to ensure accurate results and meaningful interpretations.

Base units

Biology uses the Système Internationale (SI) unit system. The fundamental SI base units you'll encounter most frequently are:

metre (m) for length, height, and distance
kilogram (kg) for mass
second (s) for time
mole (mol) for the amount of a substance

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Develop good habits by using correct abbreviations from the start. For example, seconds should be abbreviated as 's', never 'sec' or 'S'.

Derived units

Derived units are formed by combining base units. Common derived units in biology include:

square metres (m²) for area
cubic metre (m³) for volume
cubic centimetre (cm³), also written as millilitre (ml), for volume
degree Celsius (°C) for temperature
mole per litre (mol dm⁻³) for concentration of substances in solutions
joule (J) for energy
pascal (Pa) for pressure
volt (V) for electrical potential

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Note that mol dm⁻³ is the preferred unit for concentration, though the official SI derived unit is moles per cubic metre.

Non-SI units

Although examinations use SI units, you may encounter some non-SI units in biological contexts:

litre (l, L, dm³) for volume
minute (min) and hour (h) for time
svedberg (S) for sedimentation rate, used for ribosome particle size

Unit prefixes

To handle the vast range of measurements in biology, units are modified using prefixes. These prefixes represent powers of 10:

Prefix	Factor	Symbol	Example
nano	10⁻⁹	n	nanometre (nm)
micro	10⁻⁶	μ	micrometre (μm)
milli	10⁻³	m	millimetre (mm)
centi	10⁻²	c	centimetre (cm)
(whole unit)	10⁰	-	metre (m)
kilo	10³	k	kilometre (km)

Converting between units

Unit conversion allows measurements to be expressed at appropriate scales. For example, cell widths are better expressed in micrometres (μm) rather than metres to make the numbers manageable.

Basic conversion method

To convert between units, use the conversion factors based on powers of 1000:

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Going from smaller to larger units (e.g., nm → μm → mm → m → km): divide by 1000 for each step

Going from larger to smaller units (e.g., km → m → mm → μm → nm): multiply by 1000 for each step

Worked examples

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Worked Example: Basic Unit Conversions

Convert 1 m to mm: 1 × 1000 = 1000 mm

Convert 1 m to μm: 1 × 1000 = 1000 mm, then 1000 × 1000 = 1,000,000 μm

Convert 20,000 μm to mm: 20,000 ÷ 1000 = 20 mm

Converting area and volume units

Converting square units requires more care. Since 1 m² = 1000 × 1000 = 1,000,000 mm², your conversion factor becomes × or ÷ 1,000,000.

Converting cubic units requires even greater care. Since 1 m³ = 1000 × 1000 × 1000 = 1,000,000,000 mm³, your conversion factor becomes × or ÷ 1,000,000,000.

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Worked Example: Area and Volume Conversions

Convert 20 m² to km²: 20 ÷ 1,000,000 = 0.00002 km²

Convert 5,000,000 mm³ to m³: 5,000,000 ÷ 1,000,000,000 = 0.005 m³

Standard form

When working with very small numbers (like molecular dimensions), standard form (also called scientific notation) expresses numbers as powers of ten.

Standard form works by expressing numbers in the format: a × 10ⁿ, where 'a' is a number between 1 and 10, and 'n' is the power of ten.

Converting to standard form

Step 1: Write the smallest number between 1 and 10 that can be derived from your original number.

Step 2: Count how many places the decimal point must shift to return to the original number.

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Worked Example: Converting Large Numbers to Standard Form

To convert 58,900,000,000 to standard form:

Step 1: The number becomes 5.89
Step 2: Count the decimal shifts: 10 places to the right
Result: $5.89 \times 10^{10}$

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Worked Example: Converting Small Numbers to Standard Form

For small numbers like 0.0000078:

Step 1: The number becomes 7.8
Step 2: Count the decimal shifts: 6 places to the left (negative power)
Result: $7.8 \times 10^{-6}$

Significant figures

Significant figures indicate the precision of measurements and calculations.

Rule 1: All non-zero digits are significant.

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Key Points to Remember:

Always use correct SI unit abbreviations (s not sec, m not M)
Convert units to appropriate scales before calculations (μm for cell measurements)
Use conversion factors of 1000 between adjacent unit prefixes
For area conversions, use factors of 1,000,000; for volume, use 1,000,000,000
Express very large or small numbers in standard form for clarity

Appropriate Units in Calculations (AQA A-Level Biology): Revision Notes