Percentages (Animal Science)
Percentages
This page contains information about how to calculate percentages and percentage changes which you will come across in Animal Behaviour in First Year and Animal Feed Science and Technology in Second Year.
Definition
A percentage is a proportion of an amount, group or set. Another way to think of this is as a fraction out of 100. So if you had an 80% success rate at a task, this would mean that for every 100 attempts, 80 of them would be a success.
Basic calculations and background
Converting Fractions to Percentages
To convert fractions to percentages divide the numerator (number on the top) by the denominator (number on the bottom) and multiply by 100 this will give you the fraction as a percentage.
For example $\frac{5}{8}$ can be expressed as a percentage by $5\div8\times100 =62.5$%.
Worked Example 1
Worked Example - Percentages
There is a group of 56 dogs. 36% of these dogs are Spaniels, 16% are Border Collies, 10 of the dogs are Lakeland terriers, and 17 of the dogs are Newfoundlands.
a) How many of the 56 dogs are Spaniels?
b) How many are Border Collies?
c) What percentage of the 56 dogs are Lakeland terriers (to 3 s.f.)? *
d) What percentage are Newfoundlands (to 3 s.f.)?
* (“3 s.f” means “rounded to three significant figures”: include just the first three digits of a number. For example, to 3 s.f $1.032 = 1.03$).
Solution
a) 36% of the dogs are Spaniels. $56\times0.36 = 20.16 $, so 20 are Spaniels.
b) 16% of the dogs are Border collies. $56\times0.16 = 8.96$, so 9 are Border Collies.
c) 10 of the dogs are Lakeland terriers. As a percentage, this is $10 \div 56 \times 100 = 17.9\%$.
d) 17 dogs are Newfoundlands. So as a percentage this is $17\div 56 \times 100 = 30.4$%.
More complex calculations
Percentage difference
This is calculating the difference between two amounts and displaying the difference as a percentage of the average of the two numbers. To calculate this we use the formula:
\begin{equation} \frac{\text{(difference of the values)}}{\text{(mean of the values)}}\times100 = \text{ Percentage difference}. \end{equation}
See Worked Example 2 .
Calculating percentage changes
You calculate a percentage change when the amount of something you have changes. Use this method when you know the original value, the new value and you want to calculate the change as a proportion of the original amount. (you may have come across this in your animal behaviour module, as percentage improvement in inter-observer reliability)
Percentage increase:
If the amount increases then we use the formula:
\begin{equation} \frac{\text{(new value} - \text{original value)}}{\text{original value}}\times100 = \text{ Percentage increase}. \end{equation}
Percentage decrease:
If the amount decreases then we manipulate the above formula to stop it being negative by reversing the top of the fraction:
\begin{equation} \frac{\text{(original value} - \text{new value )}}{\text{original value}}\times100 = \text {Percentage decrease}. \end{equation}
Using percentage change to calculate new amounts:
This method is used when you know the percentage change and the original amount and you want to calculate how much you now have. To do this use the formula:
\begin{equation} \frac{\text{(new percentage)}}{100}\times\text{(original value)} = \text{New amount}. \end{equation}
For instance, suppose you had a poor lambing season and only had 80% of last year's total of 90 lambs. To calculate how many you had this year, substitute $80%$ as the “new percentage” and $90$ as the “original value” in the formula. That is, you have $90 \div 100 \times 80 = 72$ lambs this year.
Suppose you already had 70 cattle and your cattle numbers increased by 10%. You can calculate the new total using the formula $70 \div 100 \times 110 = 77$ cattle.
Note: This is equivalent to $70 \times 1.10 =77$. This is because percentages are a fraction out of 100 and multiplying by 1.10 is the same as dividing by 100 and multiplying by 110.
Worked Example 2
Worked Example - Percentage Change
Leo and Sandy are both young Tom cats. They were let out to hunt one night. Leo caught 5 mice and Sandy caught 7.
a) What is the mean number of mice caught by the two cats, and what is the percentage difference between them?
b) How many mice did Leo catch, as a percentage of Sandy's figure?
Test yourself
Try our Numbas test on percentages and ratios.
External links
Percentage difference at Math is Fun
See also
For further information on these topics see the main site's pages on Percentages and Ratios.
You can also perform percentage calculations quickly on your calculator see using your calculator.