 Using numbers and handling data

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# 1.7 SI units and conversions

The international system of units (Le Système International d'Unités: abbreviated to SI) was developed in France during the 18th century in an effort to create a unified and rational system of weights and measures. The SI system became adopted as the world standard in 1960.

There are seven basic units (or base units) to the SI system and these are shown in Table 3. All other units of measurement can be derived from combinations of these base SI units.

## Table 3 The seven base SI units

Quantity Name Symbol
Lengthmetrem
Masskilogramkg
Timeseconds
TemperaturekelvinK
Electric currentampereA
Luminous intensitycandelacd
Amount of substancemolemol

Many units of measurement arise from a combination of different base SI units, and some of these are given in Table 4. For instance, you will see from the table that speed is defined in 'metres per second'. This can be written as metres divided by seconds, i.e. m/s, where the slanted line indicates the act of division. Another way you may see this expressed is as m s−1 where the negative exponent indicates the division.

Similarly, the newton is a SI-derived unit of force. It is defined as the amount of force needed to accelerate a mass of 1 kg at a rate of 1 metre per second per second, and is expressed in terms of the following SI units: m kg s−2.

## Table 4 Commonly used units that are derived from base SI units

Quantity Derived unit Symbol SI units
Speedmetres per secondm s−1m s−1
ForcenewtonNm kg s−2
EnergyjouleJm2 kg s−2
Volumecubic metrem3m3
PressurepascalPakg m −1 s−2

In addition, some non-standard SI units are in common usage, and a selection of these is given in Table 5.

## Table 5 Commonly used units that are not derived from base SI units

Quantity Symbol Non-SI unit Conversion factors
Timeminminute1 min = 60 s
Timehhour1 h = 60 min = 3600 s
Timedday1 d = 24 h = 1440 min = 86400 s
Volume1litre1 l = 0.001 m3
Massttonne1 t = 1000 kg
Energycalcalorie1 cal = 4.18 J
Temperature°CCelsius1 °C = 274.15 K
PressuremmHgmillimetres of mercury1 mmHg = 133.3 Pa

When you are dealing with particularly large or small quantities, the SI system is combined with the decimal system, such that you write the decimal notation first then follow it with the relevant SI unit.

For instance, 1000 metres is 1 kilometre and this is abbreviated to 1 km. One hundredth of a metre is one centimetre, abbreviated as 1 cm.

## Box 2 A note about temperature

Although the basic SI unit of temperature is the kelvin, most people use and are familiar with degrees Celsius (°C). (Note that when using kelvins, the 'degrees' symbol '°' is not used.) These two temperature scales are equivalent, so a temperature change of 1 °C is the same actual increase or decrease as a temperature change of 1 K. The only difference is that these temperature scales don't start at the same place. The Celsius scale takes its starting point to be the temperature at which water freezes (0 °C), whilst the Kelvin scale starts from absolute zero (0 K; the coldest temperature theoretically possible, where even molecules stop moving). Zero kelvin is the same as −273.15 °C.

It is vitally important that you are comfortable with how the SI and decimal systems interact and how to make conversions within these units of measurement. In order to help you achieve this, now test yourself with practice questions 10 and 11.

Right click and open the practice questions [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] in a separate window, then you can switch easily between the course text and the questions.

Activity 1 will allow you to practise comparing quantities (in this case weights and temperatures) that are in different units of measurement. You can practise similar calculations to those you will be asked to perform in Part 1 for yourself using many common foodstuffs that list the quantities of vitamins, fats, fibre, etc. that they contain. The time you should allow to complete the three parts of the activity is 45 minutes. Please try working through the questions first before looking at the answers.

## Activity 1.1 Comparing SI units

Timing: 0 hours 25 minutes

### Part 1 Vitamin tablets

A multivitamin tablet contains various vitamins and minerals. Table 6 shows the recommended daily allowance (RDA) for a selection of them, as shown on the packet.

#### Table 6 Label from packet of vitamin tablets

Component %RDA Amount per tablet
Vitamin A100800 μg
Vitamin B61002 mg
Vitamin C10060 mg
Vitamin D1005 μg
Vitamin E10010 mg
Magnesium50150 mg

Note: although denoting micrograms as 'μg' is scientifically correct, remember that in the healthcare workplace it's generally better to write it as 'mcg' to avoid possible confusion with milligrams (mg).

Using this list, can you order the components, from the highest to the lowest amount, by the weight of the substance that equates to 100% RDA?

The first thing to notice is that not all of the units of measurement are the same, some are in milligrams (mg) and others are in micrograms (μg). It helps if you convert all the units of measurement to be the same before attempting to put them in order.

Only Vitamin A and D are expressed in micrograms, so let's convert them to milligrams. Because a microgram is 1000 times smaller than a milligram, to convert μg into mg, divide by 1000. (Remember, to divide by 1000 you can move the decimal point 3 places to the left: 1 μg = 0.001 mg).

The amount of Vitamin A present is 800 μg, or 800 ÷ 1000 = 0.8 mg. This is the full RDA (100%), so the RDA is 0.8 mg.

The amount of Vitamin D present is 5 μg, or 5 ÷ 1000 = 0.005 mg. Again, this is the full RDA, so the RDA is 0.005 mg.

The amount of magnesium present is 150 mg. However, this is only half of the RDA (50%), so the full RDA is twice this amount:

150 mg x 2 = 300 mg

Therefore, in order of decreasing RDA, the components should read: magnesium (300 mg), vitamin C (60 mg), vitamin E (10 mg), vitamin B6 (2 mg), vitamin A (0.8 mg), and vitamin D (0.005 mg).

## Activity 1.2 Comparing SI units

Timing: 0 hours 5 minutes

### Part 2 Temperature

What is the freezing point of water on the Kelvin scale?

The freezing point of water is 0 °C, which is +273.15 K.

## Activity 1.3 Comparing SI units

Timing: 0 hours 15 minutes

### Part 3 Temperature

What is the normal range of human body temperature in degrees Celsius? Why is there a range of values?

Body temperature varies with age, time of the day, menstrual cycle and location in the body: in a 6-year-old the temperature can vary by around 1 °C per day; your temperature is generally highest in the evening; ovulation can increase the temperature by about 0.6 °C; the body core (gut, liver) is generally warmer than the periphery (arms, legs). Bearing all this in mind, the range 36.5-37.2 °C is considered normal for a healthy person. 38 °C or above is a significant fever.

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