A.0 Arithmetic and numerical computation

Write the quantity, unit and time or area basis before calculating. Convert units first, then substitute values and report a final answer with the correct magnitude and significant figures.

Convert cm³ to dm³ only after identifying the required output; a cardiac output of 3,750 cm³ min⁻¹ is 3.75 dm³ min⁻¹.

A numerically plausible answer with incompatible units is still wrong.

Standard form writes a number as a × 10ⁿ with 1 ≤ a < 10. It makes very small cells, concentrations and large population counts easier to compare and calculate.

0.00045 m becomes 4.5 × 10⁻⁴ m; when multiplying, multiply coefficients and add powers of ten, then check whether the result’s scale fits the biological context.

Changing notation does not change the quantity, and rounding too early can distort a later ratio.

A ratio compares quantities on the same basis; a percentage expresses a part relative to a stated whole. Keep the order of the ratio explicit before calculating.

Simplify a ratio only after converting units. For a percentage change, divide the change by the original value, not the final value.

If a culture rises from 40 to 50 cells, the increase is 10/40 × 100 = 25%, whereas the new value is 125% of the original.

A ratio of 2:1 is not the same claim as “twice as many” unless the numerator and denominator are clearly defined.

An estimate gives the expected scale of a result before exact calculation. It is a reasonableness check, not a replacement for showing the measured or calculated value.

Round inputs to one useful figure, keep powers of ten visible and compare the exact answer with the estimate; investigate a large mismatch.

A 2.0 cm² leaf area with a flux near 5 units cm⁻² h⁻¹ should produce a total near 10 units h⁻¹, not 10,000.

Do not use rough rounding when a small difference is the biological conclusion.

Powers describe repeated multiplication; exponentials model multiplicative change; logarithms reverse exponentiation and turn products into sums. Identify which quantity is changing before choosing a form.

For growth or decay, compare ratios across equal time intervals. A logarithmic transform is useful when a relationship becomes linear after taking logs.

A tenfold increase changes log₁₀(x) by 1, while doubling changes it by log₁₀2, not by 2.

A logarithmic scale compresses differences; equal distances on the graph do not mean equal absolute changes.

SI prefixes change the scale of a unit: milli is 10⁻³, micro 10⁻⁶, nano 10⁻⁹ and kilo 10³. Convert to one common unit before comparing or substituting.

Write the prefix as a power of ten, cancel units algebraically and check whether the direction of the conversion makes sense.

250 μm = 250 × 10⁻⁶ m = 2.50 × 10⁻⁴ m; it is smaller than 250 mm, not larger.

The prefix belongs to the unit, not to the numerical value; mixing μm and mm can create a thousand-fold error.