5.3.2Tools
Using Units, Symbols and Numerical Values in Biology — IB Biology SL Revision Notes & Topical Questions
5 min read 6 parts Lesson 8 of 10
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Section 1 of 6SI Units
Every measurement should have a number and a unit.
Base units
- Base units Length in metres, mass in kilograms, time in seconds, temperature in kelvin and amount of substance in moles.
Derived units
- Derived units Examples are the pascal for pressure, the joule for energy and the cubic metre for volume.
Common biological units
- Common biological units Biology often uses the degree Celsius, minutes and hours, grams, cm³ and dm³.
Symbols
- Symbols Use correct symbols such as m, g, s and mol, which are not pluralised or followed by a full stop.
Section 2 of 6Prefixes and Conversions
Prefixes and Conversions
kilo (k)
- kilo (k) 10³, so 1 km = 1000 m.
centi (c) and milli (m)
- centi (c) and milli (m) 10⁻² and 10⁻³, so 1 cm = 0.01 m and 1 mm = 0.001 m.
micro (μ)
- micro (μ) 10⁻⁶, so 1 μm = 0.000001 m and 1000 μm = 1 mm.
nano (n)
- nano (n) 10⁻⁹, so 1 nm = 0.000000001 m, useful for molecules and viruses.
Volume
- Volume 1 cm³ is the same as 1 mL, and 1 dm³ is the same as 1 litre.
| Convert | Method |
|---|---|
| μm to mm | Divide by 1000 |
| mm to μm | Multiply by 1000 |
| g to kg | Divide by 1000 |
Section 3 of 6Significant Figures
1
All non-zero digits are significant, and zeros between non-zero digits are significant.
2
Leading zeros before the first non-zero digit are not significant, so 0.00079 has two significant figures.
3
Trailing zeros after a decimal point are significant, so 689.0 has four significant figures.
4
To round, count from the first significant figure and look at the next digit; if it is 5 or more, round up.
5
Give an answer to no more significant figures than the least precise of the data used.
Section 4 of 6Presenting Numbers
Scientific notation
- Scientific notation Very large or small numbers are written as a × 10ⁿ, such as 6.02 × 10²³.
Consistent precision
- Consistent precision All values in a data set should have the same number of decimal places.
Table headings
- Table headings Put the unit in the heading, not in each cell, for example Length / mm.
Avoid the word amount
- Avoid the word amount In science, amount means moles; use mass, volume or concentration instead.
Section 5 of 6Worked Example
Question
- A cell is 25 μm long.
- Express the length in mm and in metres using scientific notation.
- Also round 0.004072 mol dm⁻³ to two significant figures.
- Convert μm to mm by dividing by 1000: 25 ÷ 1000 = 0.025 mm.
- 1 μm = 10⁻⁶ m, so 25 μm = 25 × 10⁻⁶ m = 2.5 × 10⁻⁵ m.
- For 0.004072 the first significant figure is 4, and the second is 0;
- the next digit is 7, so round the 0 up to 1.
- The rounded value is 0.0041 mol dm⁻³.
Answer
- 0.025 mm;
- 2.5 × 10⁻⁵ m;
- 0.0041 mol dm⁻³.
Section 6 of 6Exam Checklist & Tips
5.3.2 – Key Points for the Exam
- SI unit A unit of the International System, the standard for science.
- Prefix A letter added to a unit to show a power of ten.
- Significant figure A digit that is reliable and needed to show the size of a quantity.
- Scientific notation A way of writing numbers as a × 10ⁿ.
Common Mistakes
- Writing units in the wrong case, such as Mm for mm; these differ by a factor of a billion.
- Counting leading zeros as significant figures.
- Giving answers to far more significant figures than the data justify.
- Mixing units in one calculation without converting them first.
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