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# Mathematical skills in Life Sciences

## Mathematical skills in Life Sciences (ESG3T)

Mathematical skills are important in Life Sciences. Below are explanations of some of the skills you will encounter.

• Scales
• Averages
• Percentages
• Conversions

NB. You must state the UNITS at the end of each calculation, e.g. cm, degrees, kg, etc.

### Scales (ESG3V)

A scale is given in a diagram, drawing or electron micrograph so that the actual size of the object that is being shown can be determined. The object could be bigger or smaller in real life.

Example: To measure the diameter of a chloroplast with a scale line of 1 µm.

1. Measure the length of the scale line on the micrograph in mm, e.g. 1 µm = 17mm

2. Measure the diameter of the organelle in millimetres, e.g. = 60mm

3. True diameter of chloroplast:

\begin{align*} &= \frac{\text{measured size } \times \text{ true length of scale line}}{\text{measured length of scale line}} \\ &= \frac{ \text{60}\text{ mm} \times \text{1}\text{ μm}}{\text{17}\text{ mm}} \\ &= \text{3,53}\text{ μm} \end{align*}

Answer: The true diameter of the chloroplast is 3.53 μm.

### Averages (ESG3W)

To find an average of a set of numbers, you add all the items and divide the total by the number of items.

Example: Find the average height in a class of 10 learners with the following heights in cm: 173, 135, 142, 167, 189, 140, 139, 164, 172, 181 cm.

1. Add all 10 learners heights together to get a total.
2. Divide the total by the number of learners (10) to get the average.

Total:

\begin{align*} \text{Sum } &= \text{1 602}\text{ cm} \end{align*}

Average:

\begin{align*} \text{Average } &= \frac{1602}{10} \\ &= \text{160,2}\text{ cm} \end{align*}

Answer: The average height of the learners is 160,2 cm

### Percentages (ESG3X)

To calculate a percentage, multiply the fraction by 100.

Formula for calculating percentage ($$\%$$):

$\text{Percentage } = \frac{\text{Number with feature }(A)}{\text{Total number }(B)} \times 100$

Example:There are 48 learners and 4 of them are left handed. Calculate the percentage of learners in your class that are left-handed.

1. Count how many learners are left handed (A).
2. Count the total number of learners in the class (B).
3. Divide the number of left-handed learners (A) by the total number of learners (B) to get a fraction or proportion.
4. Multiply the fraction by 100.

Therefore, to calculate the percentage of learners that are left-handed:

\begin{align*} &= \frac{A}{B} \times 100 \\ &= \frac{4}{48} \times 100 \\ &= \text{8,3}\% \end{align*}

Answer: $$\text{8,3}\%$$ of the learners in your class are left-handed.

Example: Using the same class of learners, calculate the percentage of learners that are right-handed.

To calculate the percentage of the class that is right handed, one could count the number of right-handed students, and perform the percentage calculation again. Or, since the whole class is equal to 100 %, one can simply subtract the percentage of left-handed students and you will be left with the percentage of right-handed students.

The percentage of right-handed learners:

\begin{align*} &= 100 - \text{8,3} \\ &= \text{91,7}\% \end{align*}

Answer: $$\text{91,7}\%$$ of the learners in your class are right-handed.

### Conversions (ESG3Y)

Below is a table with some common conversions that you will need to use in the study of Life Sciences:

 From unit: To unit (number of these units per “From unit”): m mm µm nm m $$\text{1}$$ $$\text{1 000}$$ $$\text{1 000 000}$$ $$\text{1 000 000 000}$$ mm $$\text{10}^{-\text{3}}$$ or 1/$$\text{1 000}$$ $$\text{1}$$ $$\text{1 000}$$ $$\text{1 000 000}$$ µm (micrometres) $$\text{10}^{-\text{6}}$$ or $$\frac{1}{\text{1 000 000}}$$ $$\text{10}^{-\text{3}}$$ or $$\frac{1}{\text{1 000}}$$ $$\text{1}$$ $$\text{1 000}$$ nm (nanometres) $$\text{10}^{-\text{9}}$$ or $$\frac{1}{\text{1 000 000 000}}$$ $$\text{10}^{-\text{6}}$$ or 1/$$\text{1 000 000}$$ $$\text{10}^{-\text{3}}$$ or $$\frac{1}{\text{1 000}}$$ $$\text{1}$$