FBE05 – Mathematics and Statistics Lecture 2 - Unit measurement and basic instrument

Units of measurement, in one form or another, have been with us for many centuries. It is quite likely that the units for length and mass were the first ones to be invented. Our ancestors used the body parts as measuring instruments. Early Babylonian, Egyptian and other records indicate that length was measured with the forearm, hand or fingers. As civilizations evolved, units of measurement became more complicated to cater for trade, land division, taxation and other uses. Conversion of units may be done using a range of methods: (a) Conversion factors (b) Tables (c) Graphs

Conversion factors

Conversion factors (a) 56 mm into metres (b) 445 mm into metres (c) 5.4 m into centimetres (d) 2 ft 5 in into millimetres (e) 4 yd into metres (f) 10 in into metres

Conversion factors

Graphical method A graph can be plotted for any two units, and the resulting straight line used to convert one unit to the other. Figure 2.1 shows a graph that can be used to convert metres into feet and vice versa. Known conversion factors are used to plot the straight-line graph: 1 ft = 0.3048 m 10 ft = 3.048 m 20 ft = 6.096 m 30 ft = 9.144 m 40 ft = 12.192 m

Graphical method In Figure 2.1 the x-axis is used for metres and y-axis for feet; however, the choice of an axis for a particular unit is immaterial. Using the scale shown in Figure 2.1, plot 4 points having the coordinates (3.048, 10), (6.096, 20), (9.144, 30), and (12.192, 40). Draw a straight line through all the points. This graph can be used to convert feet into metres and vice versa, as shown:

Graphical method

Graphical method Draw a graph between feet and metres and use it to convert: (a) 15 ft into metres (b) 5 m into feet

Comparison Conversion factors with Graphical method Convert: (a) 0.050 kg into grams (b) 20 500 kg into tonnes (c) 505 g into ounces

Conversion factors

Graphical method As explained a straight-line graph can be plotted between two units and used to convert one unit into the other. Figure 2.2 shows a graph that can be used to convert kilograms into pounds and vice versa. Known conversion factors are used to plot the straight-line graph: 1kg = 2.20462lb 10 kg = 22.0462lb 20 kg = 44.0924lb 30 kg = 66.1386lb