Eukaryotes and prokaryotes: Students should be able to demonstrate an understanding of the scale and size of cells and be able to make order of magnitude calculations, including the use of standard form.

The idea

Cells vary greatly in size, so biologists use a common unit, the micrometre (µm), where 1 µm = 1 × 10⁻⁶ m. A typical bacterium is about 1–5 µm, a human cheek cell about 50–100 µm, and some eukaryotic cells are larger still. An order of magnitude is a factor of ten, so comparing sizes means asking how many powers of ten apart two values are. To do this, write each size in standard form, A × 10ⁿ, then compare the powers n. For example, 2 µm = 2 × 10⁻⁶ m and 80 µm = 8 × 10⁻⁵ m; the powers differ by one, so the cheek cell is about one order of magnitude, roughly ten times, larger. If the powers differ by two, the sizes differ by about one hundred times. Always convert to the same unit before comparing, and give the answer as a factor or a power of ten.

What earns the marks

• Uses the micrometre as a suitable unit for cell size and converts correctly between micrometres and metres using 1 µm = 1 × 10⁻⁶ m.
• Writes cell sizes in standard form as A × 10ⁿ, where A is between 1 and 10, for example 5 µm = 5 × 10⁻⁶ m.
• Compares two sizes by finding the difference between their powers of ten and expressing the result as an order of magnitude, such as about 10 times or about 100 times larger.
• Converts both measurements to the same unit before dividing or comparing, avoiding mixing micrometres with millimetres or metres.
• Interprets an order of magnitude as a factor of ten and applies this to realistic cell sizes, for example a 2 µm bacterium against an 80 µm cheek cell.
• Communicates the final comparison clearly, stating whether one cell is larger and by roughly how many orders of magnitude.

Common mistakes and how to put them right

• Mixing units, such as comparing 5 µm with 0.05 mm without converting.

  Put it right: Convert both values to the same unit, for example both to metres, before comparing.

• Writing standard form incorrectly, such as 12 × 10⁻⁶ instead of 1.2 × 10⁻⁵.

  Put it right: The number before the power of ten must be at least 1 and less than 10.

• Treating a difference of one power of ten as a difference of one unit rather than a tenfold difference.

  Put it right: Each step in the power of ten represents a factor of ten.

• Subtracting the sizes directly, for example 80 − 2 = 78, and calling this the order of magnitude.

  Put it right: Divide the larger by the smaller, or compare the powers of ten, to find the factor.

Exam tips

• Show every conversion step, including the unit you are converting to, so the examiner can follow your reasoning even if the final value is slightly out.
• When asked for an order of magnitude, give a factor such as about 10 times or about 100 times, and support it by quoting the powers of ten you compared.
• Check that your standard form has one non-zero digit before the decimal point, and use the correct sign on the power of ten for small measurements.