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Mathematical Skills in Biology

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”):
 mmmµmnm
m110001 000 0001 000 000 000
mm10−3 or 1/1000110001 000 000
µm (micrometres)10−6 or 1/1 000 00010−3 or 1/100011000
nm (nanometres)10−9 or 1/1 000 000 00010−6 or 1/1 000 00010−3 or 1/10001

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