Succeed with maths: part 2

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# 2 The International System (SI)

One major advantage to the SI is that everything you could ever want to measure can be measured using a few basic units, or combinations of them. As well as this, the different sizes of units to measure the same quantity, such as a distance, are all based upon the number ten. This makes calculations with SI units relatively straightforward compared to the imperial system, where there was no standard relationship between units, as you’ll see later.

Most of the scientific and engineering world agreed to use the SI system to standardise their work. However, there are some important exceptions to this, and the USA is one of these. This means that it is very important to check the units being used if an international team is working on a project, as the following costly example demonstrates:

In 1999, a NASA Mars Orbiter spacecraft was destroyed on arrival in the Martian atmosphere at a loss of \$125 million. An inquiry established that the flight system software on board the Orbiter was written to calculate thruster performance in metric newtons (N), but mission control on earth was inputting course corrections using the imperial measure, pound-force (lbf). One newton is about 0.22 pounds-force, so there was a considerable difference between the two. An expensive mistake to make!

The SI system works with a combination of base units and prefixes. An example of a base unit is the metre – this is the unit of measurement on which the other length units are based. You may well recognise some of prefixes, such as ‘kilo-’, ‘centi-’ and ‘milli-’. Combined with the metre, these give kilometre, centimetre and millimetre respectively. All these prefixes have specific numerical meanings, as shown below:

• ‘kilo-’ a thousand or 1000
• ‘centi-’ a hundredth or 0.01
• ‘milli-’ a thousandth or 0.001.

When they are added to a base unit, such as the metres in our example, they alter the size of the unit by an amount defined by the prefix.

So, kilo combined with a base unit means a thousand times the size of the base unit, centi means a hundredth of the size and milli means a thousandth of the size of the base unit.

This idea extends to cover all seven SI base units, which are shown in Table 1:

Table _unit2.2.1 Table 1 The seven base SI units
Unit name Unit abbreviation Measurement
metre m distance
kilogram kg mass
second s time
ampere A electrical current
kelvin K temperature
mole mol number of particles
candela cd light intensity

In these two weeks of study you will be using the units for distance and mass from the SI and volume from the related metric system. The SI unit for volume is based upon the metre, but in everyday situations the litre is used, since that is a more appropriate size. If you move on to study science or engineering you will come across some, if not all, of the other SI base units.

For now though, it is time to look at measurements of length.

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