## Prefixes, Power & Precision

Millions and Billions, thousandths and trillionths. Numbers and more numbers. Physics is the study of the natural (physical) world, and as such uses many measurements, or constants. From the speed of light to the charge on an electron (elementary charge), From the mass of a proton to the radius of the sun, the parade of numbers marches on. The size of universe is incomprehensibly enormous (the macroscopic) and, paradoxically, reliant on the vanishingly small (the quantum):

These numbers can be gigantic or lilliputian, and to write them out in full (where possible) is an exhausting, and in some cases futile or even impossible endeavour. Nonetheless, we must have a way of writing them in sufficient accuracy. One way of doing this is to use scientific notation, by expressing the leading digits multiplied by the a power of ten. Here is a link to good explanation of how to work with scientific notation.

While this is good, it is not enough. To explain, let’s look at age. I am 33 years, 6 months and (currently) 17 days old. In physics, time is measured in seconds, so this converts to 1057213348 seconds (online age calculator).  To say this out loud, you would say “One billion, fifty-seven million, two hundred and thirteen thousand, three hundred and forty-eight seconds”. Quite a moutful! In scientific notation, we could trim this to 1.057 x 109 seconds which is said as “One point zero five seven times ten to the ninth power”. This is better, yet we can do even better. While scientific notation is a mathematical shorthand for expressing large numbers, metric prefixes are the verbal shorthand.

Some of these metric prefixes may be familiar to you – for example, the prefix kilo, as found in kilogram or kilometre or kilolitre, in each case meaning 1000 of the basic unit (gram, metre or litre). To go back to our example of my age, we can express it as “One point zero five seven gigaseconds” or, in writing, “1.057 Gs”. There! Much easier. You should know all prefixes between Tera and Pico.

You should check out the related videos for the above video if you are finding this difficult, or you don’t remember some of the underlying maths.

Whew! Finally, we come to the issue of precision, or as discussed in Physics, significant figures. This is covered well in the followings articles on wikipedia: Significant Figures, Significance Arithmetic and Rounding. Finally, here is a short video that looks at using significant figures in class (it runs to fast, you will have use the pause function to read each screen!)

See you in class!

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### 3 Comments on “Prefixes, Power & Precision”

1. Lynette Says:

What is also a bit of a contradiction is the fact that in every day language the word ‘quantum’ is often used to describe a significant amount e.g. “There is a quantum leap between year ten and year eleven maths,” whereas in physics it means the opposite.

Is scientific notation on the maths syllabus this year?

2. mrgrichting Says:

Hi Lynette,

Sorry for the late comment, but yes it is – in second semester. The use of quantum is tricky – in the case you are using it means discrete; clearly different. So when they say there is a quantum leap, they mean that you can’t transition easily – it requires a great effort to change. Quantum physics deals with quantum phenomena that are both minuscule and discrete – most times people think that it is only referring the small, when it actually refers to both!

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