Comparing sizes
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 A number, to the base ten, often used to make comparisons. For each order of magnitude, a number is ten times the previous one.. 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 Human Immunodeficiency Virus, a disease which damages cells in the immune system. 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 km | Largest unit |
| 1,00 cm (cm = centimetres) | 1 m | |
| 10 mm (mm = millimetres) | 1 cm | |
| 1,000 mm | 1 m | |
| 1,000 µm (µm = micrometres) | 1 mm | |
| 100 nm (nm = nanometres) | 1 µm | Smallest unit |
| This many… | 1,000 m (m = metres) |
|---|---|
| …equals this many | 1 km |
| Largest unit |
| This many… | 1,00 cm (cm = centimetres) |
|---|---|
| …equals this many | 1 m |
| This many… | 10 mm (mm = millimetres) |
|---|---|
| …equals this many | 1 cm |
| This many… | 1,000 mm |
|---|---|
| …equals this many | 1 m |
| This many… | 1,000 µm (µm = micrometres) |
|---|---|
| …equals this many | 1 mm |
| This many… | 100 nm (nm = nanometres) |
|---|---|
| …equals this many | 1 µm |
| Smallest 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.