# Formulas: Units

## Contents

## Writing units

In the **Formulas question**, the writing of the unit symbols differs slightly from that in the **SI** because units are entered very simply on the computer. The rules for entering units in the **Formulas question** are described below.

- The multiplication of unit symbols is indicated by a space, as prescribed in Section 5.1 of
**SI**.*The half-high (centred) dot (⋅) is not supported*. For example, input 50 kN m (≡ 50 kN⋅m), as follows:

50 kN m

- Division of unit symbols is indicated by a solidus (oblique stroke, /) or by negative exponents.For example, input 10 m/s, or 10 m s
^{-1}, as follows:

10 m/s or 10 m s^(-1)

- Exponentiation is indicated by the circumflex accent (^, UTF-8 ﹠#94; or ASCII code 94 (alt+94)).For example, input 4.7 m
^{2}, as follows:

4.7 m^2

- Parentheses are required when there is a risk of misinterpretation. For example,
**do not input 8 kN m^-2**but rather:

8 kN m^(-2)

- Permutations of the unit symbols are allowed. For example, the following two entries are considered identical:

3 m kg s^(-2) or 3 kg m/s^2

## Defining units

Units are defined on the **Formulas question** page, in the following three places:

- For each part, in the
**Unit**field. - For each part, in the
**Other rules**field. - Under
**Extra options**, in the**[Global] - Basic conversion rule**field.

### Unit field

Specify a single or a combined unit.

kg N m/s^2

You can also specify single and combined units separated by =.

In order to accept N and kg m/s^{2} as valid units, define **Unit** as follows:

N = kg m/s^2

Note that /s^2 must be placed at the end of the unit. Hence, N = /s^2 kg m and N = kg /s^2 m will lead to an error.

With the above setting, the following units will be considered correct:

N kg m/s^2 kg m /s^2 m kg /s^2 m kg s^(-2) s^(-2) kg m s^(-2) m kg

In order to accept W, J/s and m^{2} kg s^{-3} as valid units, specify:

W = J/s = m^2 kg s^(-3)

### Other rules field

Add prefixes that are not defined in the **[Global] - Basic conversion rule** by writing units followed by a list of prefixes.

Specify that meganewton (MN) is an acceptable unit by writing the following:

N: M;

Add conversions of single units by equating their values.

1 m = 39.3700787 in;

With the above conversion rule, the following answers are equivalent:

10 in 0.254 m 25.4 cm 254 mm

### [Global] - Basic conversion rule field

Select a basic conversion rule. Prefixes and conversion factors for different basic rules are defined in the flle **conversion_rules.php**. In the file downloaded from the **Moodle plugins directory**, two rules are defined: **None** and **Common SI units**.

#### None

Select **None** if other rules contradicts the rule defined in **[Global] - Basic conversion rule** if any.

#### Common SI units

The **Common SI units** rule defines prefixes and conversion factors commonly used by physicists. The rule is as follows:

//Prefixes m: k d c m u n p f; s: m u n p f; g: k m u n p f; mol: m u n p; N: k m u n p f; A: m u n p f; J: k M G T P m u n p f; eV: k M G T P m u; W: k M G T P m u n p f; Pa: k M G T P; Hz: k M G T P E; C: k m u n p f; V: k M G m u n p f; ohm: m k M G T P; F: m u n p f; T: k m u n p; H: k m u n p; //Conversion factors J = 6.24150947e+18 eV;

Note that, for example, m: k c d m u n p f; is equivalent to:

1 m = 1e-3 km = 1e1 dm = 1e2 cm = 1e3 mm = 1e6 um = 1e9 nm = 1e12 pm = 1e15 fm;.

As the **Common SI units** prefixes and conversion factors concern mainly physicists, the rule could be renamed **Physics Units**.

With the **Common SI units** rule, the following answers are equivalent:

5 s 0.2 m/s 1 m^2 5000 ms 200 mm/s 10000 cm^2 5e9 ns 1e-6 km^2

### User defined rules

Other rules can be defined in the file **conversion_rules.php**.

Define a rule for *structural engineering* in the SI and US system of units:

$basic_unit_conversion_rules[101] = array('Structural Engineering',' // Prefixes m: k c m ; N: k M; Hz: k; s: m; // Conversion factors 1 m = 3.28084 ft; 1 ft = 12 in; 3 ft = 1 yd; 1 kg = 0.001 t; 1 N = 0.22481 lb; 1 lb = 0.001 kip; etc. ');