1.3 Units  (Page 6/6)

Two other useful conversions

Very often in Science you need to convert speed and temperature. The following two rules will help you do this:

Converting speed When converting km $·$ h ${}^{-1}$ to m $·$ s ${}^{-1}$ you divide by 3,6. For example 72 km $·$ h ${}^{-1}$ $÷$  3,6 = 20 m $·$ s ${}^{-1}$ .

When converting m $·$ s ${}^{-1}$ to km $·$ h ${}^{-1}$ , you multiply by 3,6. For example 30 m $·$ s ${}^{-1}$ $\times$ 3,6 = 108 km $·$ h ${}^{-1}$ .

Converting temperature Converting between the kelvin and celsius temperature scales is easy. To convert from celsius to kelvin add 273. To convert from kelvin to celsius subtract 273. Representing the kelvin temperature by $T_K$ and the celsius temperature by $T_{{}^{o}C}$ ,

A sanity test

A sanity test is a method of checking whether an answer makes sense. All we have to do is to take a careful look at our answer and ask the question Does the answer make sense?

Imagine you were calculating the number of people in a classroom. If the answer you got was 1 000 000 people you would know it was wrong — it is not possible to have that many people in a classroom. That is all a sanity test is — is your answer insane or not?

It is useful to have an idea of some numbers before we start. For example, let us consider masses. An average person has a mass around 70 kg, while the heaviest person in medical history had a mass of 635 kg. If you ever have to calculate a person's mass and you get 7 000 kg, this should fail your sanity check — your answer is insane and you must have made a mistake somewhere. In the same way an answer of 0.01 kg should fail your sanity test.

The only problem with a sanity check is that you must know what typical values for things are. For example, finding the number of learners in a classroom you need to know that there are usually 20–50 people in a classroom. If you get and answer of 2500, you should realise that it is wrong.

The scale of the matter... :

Try to get an idea of the typical values for the following physical quantities and write your answers into the table:

Summary

1. You need to know the seven base SI Units as listed in [link] . Combinations of SI Units can have different names.
2. Unit names and abbreviations are written with lowercase letter unless it is named after a person.
3. Rounding numbers and using scientific notation is important.
4. [link] summarises the prefixes used in Science.
5. Use figures [link] and [link] to convert between units.

End of chapter exercises

1. Write down the SI unit for the each of the following quantities:
   1. length
   2. time
   3. mass
   4. quantity of matter
2. For each of the following units, write down the symbol and what power of 10 it represents:
   1. millimetre
   2. centimetre
   3. metre
   4. kilometre
3. For each of the following symbols, write out the unit in full and write what power of 10 it represents:
   1. $\mu$ g
   2. mg
   3. kg
   4. Mg
4. Write each of the following in scientific notation, correct to 2 decimal places:
   1. 0,00000123 N
   2. 417 000 000 kg
   3. 246800 A
   4. 0,00088 mm
5. Rewrite each of the following, accurate to two decimal places, using the correct prefix where applicable:
   1. 0,00000123 N
   2. 417 000 000 kg
   3. 246800 A
   4. 0,00088 mm
6. For each of the following, write the measurement using the correct symbol for the prefix and the base unit:
   1. 1,01 microseconds
   2. 1 000 milligrams
   3. 7,2 megameters
   4. 11 nanolitre
7. The Concorde is a type of aeroplane that flies very fast. The top speed of the Concorde is 2 172 km $·$ hr ${}^{-1}$ . Convert the Concorde's top speed to m $·$ s ${}^{-1}$ .
8. The boiling point of water is 100 ${}^{\circ }$ C. What is the boiling point of water in kelvin?