Eukaryotic and prokaryotic cells

Cells contain genetic material made of DNA, but they differ in where that DNA is found. In a eukaryotic cell, the DNA is enclosed within a nucleus. In a prokaryotic cell, the DNA is not enclosed within a nucleus.

Both types of cell have cytoplasm and a cell membrane. The cell membrane forms a boundary around the cytoplasm and controls the movement of substances into and out of the cell.

Prokaryotic cells

Bacterial cells are prokaryotic and are much smaller than plant and animal cells. A bacterial cell has cytoplasm and a cell membrane, with a cell wall surrounding the membrane.

A bacterial cell has no nucleus enclosing its genetic material. Its main DNA forms a single loop in the cytoplasm. It may also contain one or more plasmids: small rings of DNA separate from the main DNA loop. Plasmids are not present in every bacterial cell.

Cell size and orders of magnitude

Cell dimensions are very small lengths, so they are often measured in micrometres or nanometres rather than metres. To compare two sizes reliably, first express them in the same unit.

The relationships between these units and the metre are:

1\,\mathrm{mm}=10^{-3}\,\mathrm{m},\qquad 1\,\mathrm{\mu m}=10^{-6}\,\mathrm{m},\qquad 1\,\mathrm{nm}=10^{-9}\,\mathrm{m}

A millimetre contains $1000,\mathrm{\mu m}$ , and a micrometre contains $1000,\mathrm{nm}$ . For example, $0.01,\mathrm{mm}$ is the same length as $10,\mathrm{\mu m}$ .

Standard form for cell sizes

Standard form expresses a positive measurement as $a\times10^n$ , where $1\leq a<10$ and $$$n$$$ is an integer. For example, $0.000009,\mathrm{m}$ is $9\times10^{-6},\mathrm{m}$ .

A negative power of ten represents a fraction of a unit: $10^{-6}$ means one millionth. The negative exponent does not mean that the length itself is negative.

Comparing cell sizes

A ratio tells us how many times larger one linear dimension is than another. Convert the measurements to the same unit, then divide the larger size by the smaller size. For measurements in standard form, divide the coefficients and subtract the exponents:

\frac{a\times10^m}{b\times10^n}=\frac{a}{b}\times10^{m-n}

For example, compare a cell dimension of $9,\mathrm{\mu m}$ with one of $100,\mathrm{nm}$ . In metres, these are $9\times10^{-6},\mathrm{m}$ and $1\times10^{-7},\mathrm{m}$ . Their ratio is:

\frac{9\times10^{-6}}{1\times10^{-7}}=9\times10^1=90

The first dimension is therefore 90 times the second. This ratio compares lengths, not areas or volumes.

Orders of magnitude

An order of magnitude is a factor of ten. A ratio of exactly $$$10^k$$$ represents a difference of $$$k$$$ orders of magnitude. For an approximate comparison, express the ratio as an approximate power of ten.

In the example, $$$90$$$ is approximately $$$10^2$$$ , so the dimensions differ by approximately two orders of magnitude. The coefficients matter: comparing only the exponents in $9\times10^{-6}$ and $1\times10^{-7}$ would miss the factor of $$$9$$$ .

An additive difference and a ratio answer different questions. The two dimensions differ by $8.9,\mathrm{\mu m}$ , but their multiplicative difference in scale is a factor of $$$90$$$ .