Maths for A Level Biology - updated edition

Example 2 8.6 cm 3 water was measured with a 50 cm 3 burette, calibrated to 0.2 cm 3 . % error = accuracy measured length × 100 = 0.2 8.6 × 100 = 2.3 % (1 dp) This example shows that measuring the same volume in a piece of equipment with smaller graduations gives a smaller percentage error. Combining errors If a calculation depends on several readings with inherent uncertainties, the result cannot be more accurate than the largest error allows. The error in the result depends on the sum of the individual errors. Example 16.0 cm 3 oxygen, collected by displacement of water in a burette, graduated to 0.2 cm 3 , are collected in 10 minutes, measured by a stop watch, correct to +0.01 s. % error in timing = 0.01 10 × 100 = 0.1% Total percentage error = 1.3 + 0.1 = 1.4% % error in volume = 0.02 16.0 × 100 = 1.3% Rate of oxygen production = 16.0 10.0  = 1.6 cm 3  min −1 Total actual error = 1.4% × 1.6 = 1.4 100 × 1.6 = 0.02 ∴ Rate of oxygen production = 1.6 + 0.02 cm 3  min −1 In general, the result and the error are quoted to the same number of decimal places but where the ϐirst number following the decimal point is small, as shown here, then an extra decimal place is given. All the terms in a calculation should have the same unit. In calculating percentage errors, it is the errors that are important, not the factor being measured. So errors in time and volume, for example, may be combined. 2.2 Proportion 2.2.1 Surface area and volume Why are bacteria so small? Could an elephant be the size of a mouse? Could a spider be the size of a fox? Why did dragonϐlies in the Carboniferous period have a wingspan of 800mm, but today only 80mm? Biologists have asked such questions many times and the more that we understand about physics and chemistry, the more we understand that living organisms are the right size both for their structure and for the way their bodies function in the environment in which they evolved. A simple organism uses diffusion across its surface to absorb the food and oxygen it needs and to remove its waste. Gas molecules diffuse efϐiciently 2 Processed numbers 35