1.3 Units  (Page 4/6)

Using significant figures

1. Round the following numbers:
   1. 123,517 $\ell$ to 2 decimal places
   2. 14,328 km $·$ h ${}^{-1}$ to one decimal place
   3. 0,00954 m to 3 decimal places
2. Write the following quantities in scientific notation:
   1. 10130 Pa to 2 decimal places
   2. 978,15 m $·$ s ${}^{-2}$ to one decimal place
   3. 0,000001256 A to 3 decimal places
3. Count how many significant figures each of the quantities below has:
   1. 2,590 km
   2. 12,305 m $\ell$
   3. 7800 kg

Prefixes of base units

Now that you know how to write numbers in scientific notation, another important aspect of units is the prefixes that are used with the units.

Prefix

A prefix is a group of letters that are placed in front of a word. The effect of the prefix is to change meaning of the word. For example, the prefix un is often added to a word to mean not , as in un necessary which means not necessary .

In the case of units, the prefixes have a special use. The kilogram (kg) is a simple example. 1 kg is equal to 1 000 g or $1\times {10}^3$ g. Grouping the ${10}^3$ and the g together we can replace the ${10}^3$ with the prefix k (kilo). Therefore the k takes the place of the ${10}^3$ . The kilogram is unique in that it is the only SI base unit containing a prefix.

In Science, all the prefixes used with units are some power of 10. [link] lists some of these prefixes. You will not use most of these prefixes, but those prefixes listed in bold should be learnt. The case of the prefix symbol is very important. Where a letter features twice in the table, it is written in uppercase for exponents bigger than one and in lowercase for exponents less than one. For example M means mega (10 ${}^6$ ) and m means milli (10 ${}^{-3}$ ).

Here are some examples of the use of prefixes:

• 40000 m can be written as 40 km (kilometre)
• 0,001 g is the same as $1\times {10}^{-3}$ g and can be written as 1 mg (milligram)
• $2,5\times {10}^6$ N can be written as 2,5 MN (meganewton)
• 250000 A can be written as 250 kA (kiloampere) or 0,250 MA (megaampere)
• 0,000000075 s can be written as 75 ns (nanoseconds)
• $3\times {10}^{-7}$ mol can be rewritten as $0,3\times {10}^{-6}$ mol, which is the same as 0,3 $\mu$ mol (micromol)

Using scientific notation

1. Write the following in scientific notation using [link] as a reference.
   1. 0,511 MV
   2. 10 c $\ell$
   3. 0,5 $\mu$ m
   4. 250 nm
   5. 0,00035 hg
2. Write the following using the prefixes in [link] .
   1. 1,602 $\times {10}^{-19}$ C
   2. 1,992 $\times {10}^6$ J
   3. 5,98 $\times {10}^4$ N
   4. 25 $\times {10}^{-4}$ A
   5. 0,0075 $\times {10}^6$ m

The importance of units

Without units much of our work as scientists would be meaningless. We need to express our thoughts clearly and units give meaning to the numbers we measure and calculate. Depending on which units we use, the numbers are different. For example if you have 12 water, it means nothing. You could have 12 ml of water, 12 litres of water, or even 12 bottles of water. Units are an essential part of the language we use. Units must be specified when expressing physical quantities. Imagine that you are baking a cake, but the units, like grams and millilitres, for the flour, milk, sugar and baking powder are not specified!