Mathematical Skills In Life Sciences | Introduction To Life Sciences | Siyavula

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”):
mmmµmnm
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 \(\frac{1}{\text{1 000}}\)\(\text{1}\)