Biology 9700/12 — October/November 2018

Background Concept

Prokaryotic cells (bacteria and archaea) are typically 0.1–5 µm in diameter, with most familiar species falling between about 0.5 µm and 2 µm. Streptococcus cells are cocci (spherical), usually 0.5–2 µm across. This is one to two orders of magnitude smaller than a typical eukaryotic cell (10–100 µm), which is one of the defining contrasts between the two cell types alongside the absence of a membrane-bound nucleus and membrane-bound organelles in prokaryotes.

For unit conversion, remember:

• $1\ \text{µm} = 10^3\ \text{nm}$ (1 micrometre = 1000 nanometres)
• so $1\ \text{nm} = 10^{-3}\ \text{µm}$

Understanding the Question

The question gives the species Streptococcus as a representative prokaryote and asks which of four numerically expressed values matches its typical diameter. All four values reduce to a single size once the unit prefix is taken into account, so the test is really twofold: know the typical size of a bacterium, and check that each option converts to a sensible number.

Approach

Convert every option to a common unit (µm is convenient), then compare each to the expected ~0.5–2 µm range. The option that lands in this band is correct.

Step-by-Step Reasoning

• Option A: $7.5 \times 10^1\ \text{nm} = 75\ \text{nm} = 0.075\ \text{µm}$. This is sub-bacterial — it is roughly the size of a small virus or a large ribosome; reject.
• Option B: $7.5 \times 10^2\ \text{nm} = 750\ \text{nm} = 0.75\ \text{µm}$. This sits squarely in the middle of the typical bacterial range; accept.
• Option C: $7.5 \times 10^0\ \text{µm} = 7.5\ \text{µm}$. A 7.5 µm sphere is at the small end of eukaryotic cell sizes (e.g. a red blood cell is ~7–8 µm); too large for a typical bacterium; reject.
• Option D: $7.5 \times 10^1\ \text{µm} = 75\ \text{µm}$. A 75 µm cell would be plainly visible to the naked eye and is comparable to a human ovum; reject.

Key Takeaways

• Typical bacterium diameter: ~0.5–2 µm (or ~500–2000 nm).
• Typical eukaryotic cell diameter: ~10–100 µm.
• Quick unit conversions: $1\ \text{µm} = 10^3\ \text{nm} = 10^6\ \text{pm}$; $1\ \text{nm} = 10^{-3}\ \text{µm} = 10^{-9}\ \text{m}$.
• In MCQs with the same coefficient and different prefixes, the trap is to misread the exponent of ten and pick a value that is the right number but the wrong scale.

Common Mistakes

• Confusing the two units and reading $7.5 \times 10^2\ \text{nm}$ as $750\ \text{µm}$ (or vice versa), which would push the size into the eukaryotic range and make C or D look plausible.
• Believing all microbes are similar in size and picking C because a typical cell you might see on a school slide is eukaryotic (plant epidermal cells, for example, are 20–100 µm).
• Picking A because 75 is a memorable number, without noticing that nanometres are three orders of magnitude smaller than micrometres.

Things to Be Careful About

• Always check the unit prefix, not just the coefficient, when the options use different prefixes.
• Quote the range of typical prokaryote sizes, not a single value, when justifying — examiners award reasoning that demonstrates understanding of the range, not just a lucky conversion.
• A useful rule of thumb: bacteria ≈ $10^{-6}\ \text{m}$ (1 µm), eukaryotes ≈ $10^{-5}\ \text{m}$ (10 µm), viruses ≈ $10^{-7}\ \text{m}$ (100 nm).