Comparing sizes

The diagram shows the size of three organisms, different cells and other structures.

The diagram shows the size of three organisms, different cells and other structures.

A comparison can be used to draw a physical relationship between two or more objects.

For instance, the length of the leaf cell above is ten times the diameter of a red blood cell.

The calculation would be:

\frac{\text{70 μm}}{\text{7 μm}} = 10

These can be compared directly because both of the numbers are in the same units.

Order of magnitude

Differences in size are often described as differences in order of magnitude. That's the difference calculated in factors of 10.

If you increase a number by one order of magnitude, you are multiplying the number by 10.

If you decrease a number by one order of magnitude, you are dividing the number by 10 (which is equivalent to multiplying by 0.1).

Hence, the length of a leaf cell above is one order of magnitude larger than the diameter of a red blood cell.

Changing between units

When comparing the size of a bacterium with the HIV virus, the values given are in different units. The different units have to be converted so that they are the same.

This many……equals this many
1,000 m (m = metres)1 kmLargest unit
1,00 cm (cm = centimetres)1 m
10 mm (mm = millimetres)1 cm
1,000 mm1 m
1,000 µm (µm = micrometres)1 mm
100 nm (nm = nanometres)1 µmSmallest unit
Question

What is the width of a cheek cell compared with a Salmonella bacterium?

140 times the size. We don't need to change the units as both values are given in µm.

Calculation:

\frac{\text{70 μm}}{\text{0.5 μm}} = 140

The width of the cheek cell is two orders of magnitude larger than the width of the salmonella bacteria.

Question

How many times longer is an ant than the diameter of a human hair?

Ant = 3 mm long

Diameter of human hair = 100 µm

Convert 3 mm into µm because µm are smaller than mm.

1 mm = 1,000 µm so 3 mm = 3,000 µm

Calculation:

3,000 ÷ 100 = 30 times

The length of an ant is one order of magnitude larger than the diameter of a human hair.

When dividing numbers in standard form, we subtract the powers.