## Mathematical Skills in Biology

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

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

### Scales

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:

\(= \cfrac{\text{measured size} × \text{true length of scale line}}{\text{measured length of scale line}}\)

\(= \cfrac{60\text{ mm} × 1\text{ μm}}{17\text{ mm}}\)

\(= 3.53\text{ μm}\)

### Averages

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.

Total = 1602 (add all 10 heights together)

\(\text{Average} = \cfrac{1602}{10}\)

\(= 160.2\text{ cm}\)

**Percentages**

To calculate a percentage, multiply the fraction by 100.

Formula for calculating percentage (%):

\(\text{Percentage} = \cfrac{\text{Number with feature }(A)}{\text{Total number }(B)} × 100\)

**Example:** 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).

There are 48 learners and 4 of them are left handed.

Therefore, % of left-handed:

\(= \cfrac{A}{B} × 100\)

\(= \cfrac{4}{48} × 100\)

\(= 8.3\%\)

8.3% of the learners in your class are left-handed.

The percentage of right-handed learners:

\(= 100 \; – \; 8.3\)

\(= 91.7\%\)

91.7% of the learners in your class are right-handed.

**Some Conversions**

From unit: | To unit (number of these units per “From unit”): | |||

m | mm | µm | nm | |

m | 1 | 1000 | 1 000 000 | 1 000 000 000 |

mm | 10^{−3} or 1/1000 | 1 | 1000 | 1 000 000 |

µm (micrometres) | 10^{−6} or 1/1 000 000 | 10^{−3} or 1/1000 | 1 | 1000 |

nm (nanometres) | 10^{−9} or 1/1 000 000 000 | 10^{−6} or 1/1 000 000 | 10^{−3} or 1/1000 | 1 |