Percentages
A percentage is a proportion that shows a number as parts of a hundred. The symbol '%' means 'per cent'. 9% means 9 out of every 100, or \(\frac{9}{100}\).
Percentages are just one way of expressing numbers that are part of a whole. These numbers can also be written as fractions or decimals.
50% can also be written as a fraction, \(\frac{1}{2}\) , or a decimal, 0.5. They are all the same amount.
Calculating percentages of amounts
Often we wish to calculate the percentage the value A is of value B. We do this by dividing value A by value B and multiplying by one hundred.
Example 1
Twenty-three students out of thirty passed their end of unit test. What percentage is this?
\(\frac{23}{30} \times 100 = 77\%\)
Percentages of amounts can also be calculated by writing the percentage as a fraction or decimal and then multiplying it by the amount in question.
Example 2
Find 16% of 40.
16% is the same as \(\frac{16}{100}\).
To find 16% of 40, multiply \(\frac{16}{100}\) by 40:
\(\frac{16}{100} \times = 6.4\)
The use of calculators will be allowed to complete this sort of calculation.
This example could also be worked out by converting the percentage to a decimal.
16% is the same as 0.16. To find 16% of 40, multiply 0.16 by 40:
0.16 脳 40 = 6.4
Percentages in nutrient cycling in ecosystems
We can use the two methods above to calculate the percentages of mass that cycles through an The living organisms in a particular area, together with the non-living components of the environment.. Here is a A sequence (usually shown as a diagram) of feeding relationships between organisms, showing which organisms eat what and the movement of energy through trophic levels.:
clover 鈫 snail 鈫 thrush 鈫 sparrowhawks
Here is a pyramid of biomass that represents this food chain.
Scientists measured the biomass of each trophic level of this food chain. Their values are recorded in the table below.
| Trophic level | Organism | Biomass (g) | Mass of carbon (g) |
| 4 | Sparrowhawk | 195 | 21 |
| 3 | Thrush | 2200 | 199 |
| 2 | Snail | 20,500 | 2200 |
| 1 | Clover | 210,000 | 100,000 |
| Trophic level | 4 |
|---|---|
| Organism | Sparrowhawk |
| Biomass (g) | 195 |
| Mass of carbon (g) | 21 |
| Trophic level | 3 |
|---|---|
| Organism | Thrush |
| Biomass (g) | 2200 |
| Mass of carbon (g) | 199 |
| Trophic level | 2 |
|---|---|
| Organism | Snail |
| Biomass (g) | 20,500 |
| Mass of carbon (g) | 2200 |
| Trophic level | 1 |
|---|---|
| Organism | Clover |
| Biomass (g) | 210,000 |
| Mass of carbon (g) | 100,000 |
Worked example 1
What percentage of the sparrowhawk consists of carbon?
\(\frac{21}{195} \times 100 = 10.8%\)
Question
Calculate the percentage carbon in the other three trophic levels.
Clover
\(\frac{100,000}{210,000} \times 100 = 47.6%\)
Snail
\(\frac{2200}{20,500} \times 100 = 10.7%\)
Thrush
\(\frac{199}{2200} \times 100 = 9.0%\)
Worked example 2
Calculate the percentage transfer of carbon between the thrush and the sparrowhawk.
\(\frac{21}{199} \times 100 = 10.5%\)
Question
Calculate the percentage of carbon transferred between the snail and the thrush.
\(\frac{199}{2200} \times 100 = 9.0%\)
Worked example 3
Calculate the percentage of biomass transferred between the clover and the snail.
Question
Calculate the percentage biomass transferred between the thrush and the sparrowhawk.
\(\frac{195}{2200} \times 100 = 8.9%\)
More guides on this topic
- What happens during photosynthesis? - OCR 21st Century
- How do producers get the substances they need? - OCR 21st Century
- How do producers transport substances they need? - OCR 21st Century
- How are organisms in an ecosystem interdependent? - OCR 21st Century
- How are populations affected by conditions in an ecosystem?
- Sample exam questions - living together - OCR 21st Century