Demonstrate an understanding of the relationship between quantitative…

The idea

Cell sizes span many orders of magnitude, so biologists attach prefixes to the metre to keep numbers manageable. Milli means 10⁻³ m, so 1 mm = 1 × 10⁻³ m. Micro means 10⁻⁶ m, so 1 µm = 1 × 10⁻⁶ m and 1 mm = 1000 µm. Nano means 10⁻⁹ m and pico means 10⁻¹² m, used for viruses and molecules. Convert by multiplying by the power of ten: 5 µm = 5 × 10⁻⁶ m = 0.000005 m. Standard form writes a number as A × 10ⁿ where A is between 1 and 10. To divide, subtract indices; to multiply, add them.

For example: A 20 µm cell is 20 × 10⁻⁶ m = 2 × 10⁻⁵ m, and comparing it with a 50 nm virus (5 × 10⁻⁸ m) shows the cell is about 400 times wider.

What earns the marks

• States milli = 10⁻³ m, micro = 10⁻⁶ m, nano = 10⁻⁹ m and pico = 10⁻¹² m.
• Converts between prefixed units and metres by multiplying by the correct power of ten, e.g. 3 µm = 3 × 10⁻⁶ m.
• Writes and manipulates values in standard form A × 10ⁿ with 1 ≤ A < 10.
• Adds indices when multiplying powers of ten and subtracts indices when dividing.
• Compares two cell-scale measurements by converting both to the same unit before forming a ratio.

Common mistakes and how to put them right

• Treating micro as 10⁻³ rather than 10⁻⁶.

  Put it right by recalling that micro is one millionth of a metre.

• Writing standard form with A outside 1 to 10, such as 25 × 10⁻⁷.

  Put it right: Correct to 2.5 × 10⁻⁶.

• Adding indices when dividing powers of ten.

  Put it right by subtracting the index of the divisor.

Exam tips

• Convert every quantity to metres in standard form before comparing or calculating.
• Check the sign of each index: prefixes smaller than a metre always give negative powers.
• Estimate the order of magnitude first so an answer like 400 times is plausible before you finalise it.