In physics, we make measurements.
In many cases, those measurements may involve extremely large values, or extremely small values. To negotiate those values we use various mathematical tools to make meanings of those numbers. The following videos examines four different tools we use to allow us to manipulate numbers more effectively.
Scientific and Engineering Notation
When variables are measured, they can be incredibly small, such as the diameter of a proton (there is smaller), or can be incredibly large such as the size of our galaxy, the Milky Way.
In either case, were we to use metres as the unit the recording of those sizes would be, let's say, problematic.
For example, the diameter of a proton would be approximately = 0.000000000000001 meters !
The diameter of the Milky Way would be around 1,000,000,000,000,000,000,000 meters !!
I hope you can see the problem.
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Watch the video to learn about the rules for scientific notation, as well as the other notation used, engineering notation. |
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Worksheet
Have a go in practising the concept learned by doing this worksheet
Have a go in practising the concept learned by doing this worksheet
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Prefixes
Another useful way to describe large and small units is the use of prefixes. You may already be familiar with some of them.
The kilometer (km) is equivalent to 1000 meters (m). Therefore the prefix “kilo” means 1000 or 103. The milliliter (mL) is equivalent to 1/1000 of a litre (L). Therefore the prefix “milli” means 1/1000 or 10-3.
Hence the use of prefixes allows for the description of large and small numbers, depending on the prefix. |
Test your understanding
Here are two worksheets (though one is a bit of fun) to help practice prefixes
- Prefixes - [answers]
- Prefix Fun - [answers] - This worksheet is a bit of fun and not the be used in SERIOUS discussions
Significant Figures
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When a dimension is measured it is only measured to a certain level of precision.
For example, if you measure a piece of paper using a 30cm ruler, you may decide it is has a length of 21cm, or maybe 21.5 cm. But you are unlikely to be confident that its 21.354cm It should be evident that if you have more decimal place, in this example, as ling as your confident of the measurement, the more precise the value is. This of course also depends of the tool you use to measure it. In physics, we generally use significant figures to communicate the level of precision of a measurement. Watch the following video to get an understanding of significant figures |
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Orders of Magnitude
Order of Magnitude is a useful tool for estimation.
In this video I explain what they are and how you can use them. |
