Units and Maths Skills » Units, Prefixes and Significant Figures

Scientific words and quantities

Scientists use words with exact meanings so that everyone, everywhere, understands the same thing. In everyday talk "mass" and "weight" get mixed up. In science they are different, and an examiner will mark you down for using the wrong one. Learn the key words in each lesson and use them exactly as defined.

A quantity is something you can measure, such as length, mass, time, volume or temperature. Quantities matter because they let us compare results and spot patterns. Many quantities are measured directly with suitable equipment. Others are worked out from measured ones.

Key terms:

• Quantity: a property that can be measured, such as mass or time.
• SI unit: a unit from the international system of units that scientists all over the world agree to use.
• Prefix: a short word placed before a unit to show a multiple or fraction of it, such as kilo-.

SI units

If one scientist measured in inches and another in centimetres, comparing results would be a headache. So the SI units are used everywhere. IUPAC, the international chemistry organisation, does the same job for chemical names, so you will see names such as ethanol and sulfate in your biology course. Use SI units unless there is a good reason not to.

Quantity	Base or common unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Energy	joule	J

The units you will use most are kg, g and mg for mass, km, m and mm for length, and kJ and J for energy. Sometimes a different unit is more sensible. A person's age in years is clearer than in seconds, and a cell is far too small to describe in metres.

Prefixes and powers of ten

Biology covers a huge range of sizes, from a whale to a virus. Prefixes save us writing long strings of zeros. Each prefix stands for a power of ten.

Prefix	Meaning	Power of ten
tera (T)	one million million	1012
giga (G)	one thousand million	109
mega (M)	one million	106
kilo (k)	one thousand	103
centi (c)	one hundredth	10-2
milli (m)	one thousandth	10-3
micro (µ)	one millionth	10-6
nano (n)	one billionth	10-9

So 1 kg is 1000 g, and 1 mg is one thousandth of a gram. A micrometre (µm) is one millionth of a metre. Going from a millimetre to a micrometre is a factor of 1000, which is three orders of magnitude.

Key terms:

• Power of ten: ten multiplied by itself a number of times, written with a small raised number, such as 10³ = 1000.

Converting between units

To interconvert units you multiply or divide by the right factor. Use this rule: going to a smaller unit, multiply (you need more of them). Going to a bigger unit, divide.

Do two steps in turn if you have to. To change 2.5 m into micrometres, go from m to mm (× 1000 = 2500 mm), then from mm to µm (× 1000 = 2 500 000 µm).

Significant figures

A calculator gives a long string of digits, but your measurements are only so accurate. Giving more digits than the data can support is misleading. We use significant figures (s.f.) to show how many digits are worth keeping.

Counting significant figures:

• The first non-zero digit is the first significant figure.
• Zeros between other digits count: 2034 has 4 s.f.
• Zeros at the start do not count: 0.0072 has 2 s.f.
• Zeros after a decimal point at the end do count: 40.0 has 3 s.f.

To round, look at the digit after the last one you keep. If it is 5 or more, round up. Otherwise leave the last digit as it is. So 3.14159 is 3.14 to 3 s.f.

In a calculation, give your answer to the same number of significant figures as the least precise number you used. Do not round any numbers in the middle of the working. Round only at the end.

Exam-style question

A student measures the width of a pollen grain as 0.045 mm and a cheek cell as 60 µm.

(a) Give the width of the pollen grain in micrometres. [1 mark]

(b) How many times wider is the cheek cell than the pollen grain? Give your answer to 2 significant figures. [2 marks]

(c) The student's balance reads 0.0305 g. State the number of significant figures in this reading. [1 mark]