Monday, November 1, 2010

Meh...... So Which One Was Accurate?

Imagine you are back in Ancient Greece trying to measure your farm again. Fun! Now, when we take our time machine back and use our metre stick, we find out that the length of the farm is 25.87m. However back in Ancient Greece, you didn't have the luxury of the metre stick. So thus, we go back to using our armspans.

Let's just settle with 1 armspan=1m. You settle with the length as 26 armspans because... Well, you counted 26 armspans. Now let's say we now travel to the future and use some sort of metre-sticko-whiz. And the number comes out as 29.283928347817341203497m. So which is accurate and which is precise? Here is your answer:

When something is accurate, the value/number is CLOSE to the actual measurement. So essentially it is the correctness of a measurement. However if something is precise, it is a reproducible measurement, and usually has more significant digits.

So what's the answer? 26 armspans is accurate, and 29.283928.......m is precise. An example of an accurate YET precise reading would be 28.8671023934871m.

Like how everything in this world isn't perfect, no measurement is perfect. Which concludes that no measurement is exact. It is only when we count (tangible) objects, we get exact measurements. For example, 30 people in the class. We cannot have 29.5 people, can we? That would just be awkward.

Absolute uncertainty is the expressed uncertainty in a certain measurement. So how on earth do we do something like that? Luckily, there are two methods.

Method number glorious one. Make at least three measurements when measuring whatever. Then calculate the average of all your measurements; The absolute uncertainty is the largest range between the lowest measurement measured and the highest. However there is one catch--You MUST throw away, crumble up, burn to ashes, sautee, and sprinkle over Donald Trump's combover, numbers that do not "belong". Let's say you have four measurements. 1.) 16.88 2.)19.89 3.)16.50 4.)16.94. Which is the odd one out? Obviously measurement number two must be discarded.

Method number two. Just simply determine the uncertainty of each measurement you make. Just use the eyes that God gave you, and use them to the best of your ability, and measure as precisely and accurately as you can. You should estimate at least to the 10th of a fraction of each increment on a measuring utensil. For example if a test tube went up in increments of 1, your uncertainty would be +- 0.1.

RELATIVE UNCERTAINTY This HAS to be expressed as a percent. (I learnt it the hard way by getting a mark off my assignment). The number of sig figs in a measurement indicates the relative uncertainty. Remember that the number of significant figures all certain digits plus all uncertain digits. There is a general formula for relative uncertainty: (Absolute uncertainty/estimated measurement) x 100

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