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SI units use prefixes to express especially large or small quantities. Using prefixes simplifies the expressions and standardises the terms used to describe numbers of any size.
Order of magnitude
The order of magnitude is a classification system based on the relative size of an object. In the SI system, we can say that an object is one order of magnitude larger than other objects if its measured value is ten times larger than the others. See the following examples:
A length of 20 metres is one order of magnitude larger than 1 metre, as 20 metres is more than ten times 1 metre.
How about kilograms? 10 grams is one order of magnitude larger than 1 gram, 100 grams is one order of magnitude larger than 10 grams, and 1 kilogram is one order of magnitude larger than 100 grams. There are, therefore, three orders of magnitude between the gram and the kilogram.
What are the SI symbols and their names?
Symbols simplify the writing and calculation of mathematical equations and results. There is a symbol for every SI prefix.
Symbols as prefixes exist for large and small values, and every prefix and symbol represents an order of magnitude. A familiar example is cm, the centimetre symbol. Its name means a hundredth of the length of a metre. Its order of magnitude is -2 against the metre, and its representation is 0.01.
Prefixes, symbols, orders, and names for large quantities
The SI prefix table below covers quantities that are larger than one unit.
| Table 1. Prefixes symbols and orders of magnitude or large quantities. | ||||
|---|---|---|---|---|
| Prefix | Symbol | Order of magnitude | Representation | Name |
| yotta | Y | 24 | 1,000,000,000,000,000,000,000,000 | Septillion |
| zetta | Z | 21 | 1,000,000,000,000,000,000,000 | Sextillion |
| exa | E | 18 | 1,000,000,000,000,000,000 | Quintillion |
| peta | P | 15 | 1,000,000,000,000,000 | Quadrillion |
| tera | T | 12 | 1,000,000,000,000 | Trillion |
| giga | G | 9 | 1,000,000,000 | trillion |
| mega | M | 6 | 1,000,000 | million |
| kilo | k | 3 | 1,000 | Thousand |
| hecto | H | 2 | 100 | Hundred |
| deca | da | 1 | 10 | Ten |
Prefixes, symbols, orders, and names for small quantities
The SI prefix table below covers quantities that are smaller than one unit.
| Table 2. Prefixes symbols and orders of magnitude or large quantities. | ||||
|---|---|---|---|---|
| Prefix | Symbol | Order of magnitude | Representation | Name |
| deci | d | -1 | 0.1 | tenth |
| centi | c | -2 | 0.01 | hundredth |
| milli | m | -3 | 0.001 | thousandth |
| micro | μ | -6 | 0.000,001 | millionth |
| nano | n | -9 | 0,000,000,001 | billionth |
| pico | p | -12 | 0,000,000,000,001 | trillionth |
| femto | f | -15 | 0,000,000,000,000,001 | quadrilionth |
| atto | a | -18 | 0,000,000,000,000,000,001 | quintillonth |
| zepto | z | -21 | 0,000,000,000,000,000,000,001 | sextillionth |
Using prefixes and symbols in everyday life
Here is a simple example that you might come across in the news:
You might read that there will be a new renewable power plant near your area, which, under normal conditions, will produce 300 MWh. But just how much is that?
The symbol MWh stands for megawatts per hour. M is the symbol for Mega, meaning one million. 300 MWh, therefore, are 300,000,000 watts per hour. An average light bulb, by contrast, consumes about 30 watts per hour. If you divide the power produced by the new power plant by the amount of energy consumed by the light bulb, it becomes clear that the plant will provide enough energy for 10,000,000 light bulbs per hour.
How are prefixes and orders of magnitude related?
In the SI units, a prefix is applied when a quantity is smaller or larger than the original unit by a factor of ten. Every prefix in the SI system tells us that a quantity is one order of magnitude smaller or larger than the previous one. See the following examples:
Temperature: 3 megakelvin, mega meaning 1 million. This measurement is six orders of magnitude larger than any temperature in the range of 1 to 9 kelvin.
Length: 4.5 kilometres, kilo meaning 1000. This measurement is three orders of magnitude larger than any measurement in the range of 1 to 9 metres.
Calculating relative sizes using orders of magnitude
We can also use calculations to know how many orders of magnitude some object is different to another one if we know their size. Orders of magnitude can tell us how the size of an object compares to others. This method of comparison is useful when measuring lengths or areas and approximating the results to know how accurate a measurement is. See the following example of using this approach:
A bolt used to manufacture a machine must have a width of 3 cm but can be slightly larger or smaller by 0.03 cm. If the bolt is wider than 3cm + 0.03 cm, it will not fit, and if it is smaller than 3 cm-0.03 cm, it will not be tight enough.
You can determine the relative size of the deviation allowed in the measurement by making a simple division:
\(\text{relative size} = \frac{3 \space cm}{0.03 \space cm} = 50\)
This indicates that the bolt size is 50 times larger than the deviation allowed in the bolt width. The allowed deviation, therefore, is two orders of magnitude lower than the width of the bolt. When making measurements to produce objects, two, three or even four to five orders of magnitude smaller mean more accurate pieces.
SI Prefixes - Key takeaways
- Prefixes allow us to use short, standardised names for very large and very small quantities.
- Prefixes have a symbol associated with them.
- The SI symbols have the same meaning as prefixes.
- We find quantity symbols in every discipline, from natural sciences to the arts.
- The order of magnitude helps us to know how large or small an object is compared to others.
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Frequently Asked Questions about SI Prefixes
What are SI prefixes?
SI prefixes are words used to substitute names of large or small quantities.
A list of useful prefixes for measurements larger than the unit and their values are: yotta (10^24), zetta (10^21), exa (10^18), peta (10^15), tera (10^12), giga (10^9), mega (10^6), kilo (10^3), hecto (10^2), and deka (10).
A list of useful prefixes for measurements smaller than the unit and their values are: yocto (10^-24), zepto (10^-21), atto (10^-18), femto (10^-15), pico (10^-12), nano (10^-9), micro (10^-6), milli (10^-3), centi (10^-2), and deci (10^-1).
How do you convert SI prefixes?
To convert SI prefixes, you need to know the prefix value and multiply by that quantity. An example would be converting 3 Meganewtons to newtons. You need to know that Mega is 1x10^6, so 3 Meganewtons are 3x10^6.
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