1.3 Units  (Page 2/6)

Natural units

This is the most sophisticated choice of units. Here the most fundamental discovered quantities (such as the speed of light) areset equal to 1. The argument for this choice is that all other quantities should be built from these fundamental units. Thissystem of units is used in high energy physics and quantum mechanics.

Writing units as words or symbols

Unit names are always written with a lowercase first letter, for example, we write metre and litre. The symbols orabbreviations of units are also written with lowercase initials, for example $m$ for metre and $\ell$ for litre. The exception to this rule is if the unit is named after a person, then thesymbol is a capital letter. For example, the kelvin was named after Lord Kelvin and its symbol is K. If the abbreviation of the unit that is named after a person has two letters, the second letter is lowercase, for example Hz for hertz.

Naming of units

For the following symbols of units that you will come across later in this book, write whether you think the unit is named after aperson or not.

1. J (joule)
2. $\ell$ (litre)
3. N (newton)
4. mol (mole)
5. C (coulomb)
6. lm (lumen)
7. m (metre)
8. bar (bar)

Combinations of si base units

To make working with units easier, some combinations of the base units are given special names, but it is always correct to reduceeverything to the base units. [link] lists some examples of combinations of SI base units that are assignedspecial names. Do not be concerned if the formulae look unfamiliar at this stage - we will deal with each in detail in the chaptersahead (as well as many others)!

It is very important that you are able to recognise the units correctly. For instance, the n ewton (N) is another name for the kilogram metre per second squared (kg $·$ m $·$ s ${}^{-2}$ ), while the k ilogram metre squared per second squared (kg $·$ m ${}^2$ $·$ s ${}^{-2}$ ) is called the j oule (J).

Rounding, scientific notation and significant figures

Rounding off

Certain numbers may take an infinite amount of paper and ink to write out. Not only is that impossible, but writing numbers out to a high precision (many decimal places) is very inconvenient and rarely gives better answers. For this reason we often estimate the number to a certain number of decimal places. Rounding off or approximating a decimal number to a given number of decimal places is the quickest way to approximate a number. For example, if you wanted to round-off $2,6525272$ to three decimal places then you would first count three places after the decimal. $2,652|5272$ All numbers to the right of $|$ are ignored after you determine whether the number in the third decimal place must be rounded up or rounded down. You round up the final digit (make the digit one more) if the first digit after the $|$ was greater or equal to 5 and round down (leave the digit alone) otherwise. So, since the first digit after the $|$ is a 5, we must round up the digit in the third decimal place to a 3 and the final answer of $2,6525272$ rounded to three decimal places is 2,653.