Mathematical skills in Life Sciences | Introduction to 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.

Measure the length of the scale line on the micrograph in mm, e.g. 1 µm = 17mm
Measure the diameter of the organelle in millimetres, e.g. = 60mm
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.

Add all 10 learners heights together to get a total.
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.

Count how many learners are left handed (A).
Count the total number of learners in the class (B).
Divide the number of left-handed learners (A) by the total number of learners (B) to get a fraction or proportion.
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 \(\frac{1}{\text{1 000}}\)	\(\text{1}\)

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