Units and Unit Conversion

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The Mathematics 11 Competency Test

Units and Unit Conversion

The fact of the matter is that units of measurement are an essential part of most of the numbers that we use in everyday life. The presence of these units of measurement is perhaps so common that we sometimes need not deliberately take conscious account of them. Nevertheless, they are often part of our conversation because without them, numbers usually don’t seem to be complete or make sense.

For example, suppose that only your way to the airport, you need to fuel your car – which you do at a price of 92.9 cents per litre. As you wait at the airport, you strike up a conversation with a friendly person in transit from another part of the world. Still reeling from the magnitude of your gasoline bill, you ask what the price of gasoline is in your friend’s country. “Oh,” is the reply, “it is very very expensive. Recently I paid 48.7 for gasoline!” Now, in this part of the world (Greater Vancouver, British Columbia) at this time, gasoline selling for 48.7 cents per litre would result in lines of cars stretching kilometres (or perhaps miles, leagues, stadia, furlongs, angstroms, etc.) containing people waiting to guy gasoline at such an unbelievably low price. Then it occurs to you – perhaps this is not such a cheap price because in your new friend’s country the currency system is different and also maybe the way in which they measure quantities of gasoline. So you ask, and find out specifically that the price of gasoline in his country is 48.7 dubloonitos per bucketooni. This, of course, doesn’t help much because you aren’t really sure how much money a dubloonito is, nor how much gasoline a bucketooni is. It won’t be until you can relate dubloonitos to cents and bucketoonis to litres that you will be able to assess whether what your friend pays for gasoline is either very expensive or not, compared to what you’ve just paid.

So, there are two types of issues you need to be able to deal with as far as units of measurement are concerned (in life, and for the BCIT Mathematics 11 Competency Test):

  1. you need to recognize the names or naming system we use in Canada for units of measurement, and know how to use the terminology correctly.

  2. you need to master a systematic approach to being able to convert quantities expressed in terms of one set of units to the equivalent quantity expressed in other corresponding units.

Point (1) is important because improper use of units or failing to state units causes avoidable confusion and even avoidable loss of property or life. Among examples you may have heard of are:

  1. In July, 1983, an Air Canada Boeing 767 airliner was forced to glide to an emergency completely unpowered landing at a former airfield in Manitoba after running out of fuel completely midway through a flight from Ottawa to Edmonton. Miraculously, property damage and human injury were minimal despite the fact that the abandoned runway was occupied by large numbers of spectators and participants in an automobile race meet that day. The cause of the accident was a manual calculation of fuel onboard using an incorrect conversion factor (the Boeing 767 procedures required fuel to be computed in kilograms, but the crews had actually calculated the number of pounds of fuel on board). The aircrew had checked the calculations more than three times to ensure no errors had occurred, but they used the same incorrect conversion factor each time. The truth is that it doesn’t matter how accurate your arithmetic is if the units in the calculation are being handled incorrectly.

  2. In September, 2000, NASA engineers sent an instruction to the Mars Climate Orbiter spacecraft which apparently caused it to fire control rockets in a way that unintentionally sent it crashing into the surface of Mars, and being totally destroyed. The problem: the flight engineers did their calculations with one set of units and the computers onboard the spacecraft were programmed to assume another set of units. This little error in handling units of measurement was the cause of the loss of a $125 million to $165 million spacecraft, depending on which news reports you consult. (In fact, we learn one other lesson from this story. The NASA engineers had apparently noticed previously that there were discrepancies between numbers they calculated and the corresponding values produced by the people who constructed the control computers. However, they never got around to sorting out the reason for the disagreement. This is like the common blunder of not checking the answer obtained for a problem with all available information.)

Point (2) is important because, despite the gradual adoption of the SI system of units around the world, we still live and work with many different types of units of measurement, and it is often necessary to be able to convert quantities from one set of units to another.

David W. Sabo (2003)

Units and Unit Conversion

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