Science focuses on studying how things happen in the real world—things you can see, touch, hear, smell, feel, or imagine such as time.
Fractions and decimals
Early society had primitive ideas such as one, two or many, then more sophisticated means of counting emerged, mainly relating to trade. Units of weight, volume and money were at first integer whole units, often recorded by notches in a tally stick or marks in clay tablets. About 6000 years ago, with the advent of writing came units such as the length of the king's arm, together with the idea of multiples such as dozens and scores, together with vulgar fractions based on halves, quarters and so on., In order to describe these things, it is necessary to carefully measure what is observed.
In 1791, following the French Revolution, the decimal system was published based on tens and multiples or fractions of ten. The idea of ten months per year and ten days in a week were quickly dropped, but for most purposes it was revolutionary, with integrated standard weights and measures, such as fixing the second to the length of a pendulum of one metre, and the weight of a kilo of water the same as a litre volume. Since the 1960s the International System of Units ("Système International d'Unités" in French, hence "SI") has been almost universal outside the United States of America, which still prefers a version of the Imperial Roman measuring system which emerged more than 2000 years go and which is complicated and illogical.
Measurements must always be reported with appropriate units, which specify what type of quantity is being discussed - weight, length or whatever. For science and engineering, the SI system is universal and is not 'owned' by anyone, so it remains constant and free of political manipulation. As recently as 1897 the Indiana State Legislature,attempted (unsuccessfully) to set the value of Pi to 3.2, and during 1940, in Britain, the weight of a pound (lb) loaf of bread was legislated at a lower weight to concerve supplies during food rationing, giving rise to the expression 'baker's dozen' because you needed thirteen new loaves or buns for the same quantity of bread as 12 of the correct weight!
The Measurement and the Decimal Metric System
As a simple example of the importance of units, imagine you had to make curtains and needed to buy material. The shop assistant would need to know how much material was required. Telling her you need material 2 wide and 6 long would be insufficient—you have to specify the unit (i.e. 2 metres wide and 6 metres long). Without the unit, the information is incomplete and the shop assistant would have to guess. If you were making curtains for a doll's house the dimensions might be 2 centimetres wide and 6 centimetres long!
It is not just lengths that have units. Any measurement of any physical phenomenon—time, temperature, force, or voltage, just to name a few—has units.
Tip: Many physics problems ask you to determine a specific numeric quantity. When you solve the problem, do not forget to specify the units of your answer: even if you have the right number, your answer is not correct unless you include the correct units.
In the remainder of this class we will be using SI units, which are defined in the table below. These seven units are used to measure fundamental quantities, and are the basis of everything we will do, as will be discussed in more detail in the next section.
|countable amount of substance||mole||mol|