Below are shown the prefixes (factors) used with units of lengths, mass, area, volume, .... The symbol, the name and the corresponding factor are presented in the table below. Example with each of the 12 symbols are also included. More exercises with solutions are presented at the bottom of the page.
Note several forms of the factors corresponding to the SI prefixes are given: decimal, division, fraction and power to cater for all levels. In the examples below, the calculations are done using the decimal form, however the other forms may also be used.
Definition of Prefixes
A prefix (in units) is a word that precede a basic unit, such as meter, grams ..., that indicates a multiple ( > 1 ) or fraction ( < 1) of the basic unit.
For example kilometer is made of the prefix kilo (in Greek) which means a thousand and the basic unit meter .
1 kilometer = 1000 meters
The table below shows the names of some of the mostly used prefixes, their abbreviations and the corresponding factor.
Table. 1 - Metric SI Prefixes
Examples with Solutions
Basic units such as meter (length), liter (volume), gram (mass) and Watt (power) are used in the examples below.
Example 1
Convert \( 7 \; \color{red}{\textbf{pico}} \textbf{meters} \) to meters.
Solution to Example 1
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ pico = }
0.000000000001 = 1 \div 1000000000000 \\ \qquad \qquad = \displaystyle \frac{1}{1000000000000} = 10^{-12} } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ p }} \text {for pico and the sysmbol} \textbf{ m } \text {for meters to write } \\[15pt]
7 \; \color{red}{\textbf{pico}} \textbf{meters} \\[15pt]
= 7 \; \color{red}{\textbf{p}}\textbf{m} \\[15pt]
\text {Substitute } \color{red}{\textbf{p (pico) }} \text{ by its factor and evaluate} \\[15pt]
= 7 \times \color{red}{0.000000000001} \textbf{ m} \\[15pt]
= 0.000 000 000 007 \textbf{ m} \)
Example 2
Convert \( 3.2 \; \color{red}{\textbf{nano}}\textbf{meters} \) to meters.
Solution to Example 2
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt]
\color{red}{\textbf{ nano = }
0.000000001 = 1 \div 1000000000 \\ \qquad \qquad = \displaystyle \frac{1}{1000000000} = 10^{-9} } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ n }} \text {for nano and the sysmbol} \textbf{ m } \text {for meters to write } \\[15pt]
3.2 \; \color{red}{\textbf{nano}}\textbf{meters} \\[15pt]
= 3.2 \; \color{red}{\textbf{n}}\textbf{m} \\[15pt]
\text {Substitute } \color{red}{\textbf{n (nano) }} \text{ by its factor and evaluate} \\[15pt]
= 3.2 \times \color{red}{0.000000001} \textbf{ m} \\[15pt]
= 0.000 000 0032 \textbf{ m} \)
Example 3
Convert \( 8 \; \color{red}{\textbf{micro}} \textbf{grams} \) to grams
Solution to Example 3
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt]
\color{red}{\textbf{ micro = }
0.000001 = 1 \div 1000000 \\ \qquad \qquad = \displaystyle \frac{1}{1000000} = 10^{-6} } \\[15pt]
\text {Use the symbol } \color{red}{{\boldsymbol { \mu }}} \text { for micro and the sysmbol} \textbf{ g } \text {for grams to write } \\[15pt]
8 \; \color{red}{\textbf{micro}} \textbf{grams} \\[15pt]
= 8 \; \color{red}{{\boldsymbol {\mu}}} \textbf{ g} \\[15pt]
\text {Substitute } \color{red}{{\boldsymbol { \mu \;} (micro)}} \text{ by its factor and evaluate} \\[15pt]
= 8 \times \color{red}{0.000001} \textbf{ g} \\[15pt]
= 0.000 008 \textbf{ g} \)
Example 4
Convert \( 0.4 \; \color{red}{\textbf{milli}} \textbf{liters} \) to liters.
Solution to Example 4
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt]
\color{red}{\textbf{ milli = }
0.001 = 1 \div 1000 \\ \qquad \qquad = \displaystyle \frac{1}{1000} = 10^{-3} } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ m }} \text {for milli and the sysmbol} \textbf{ L } \text {for liters to write } \\[15pt]
0.4 \; \color{red}{\textbf{milli}} \textbf{liters} \\[15pt]
= 0.4 \; \color{red}{\textbf{m}}\textbf{L} \\[15pt]
\text {Substitute } \color{red}{\textbf{m (milli) }} \text{ by its factor and evaluate} \\[15pt]
= 0.4 \times \color{red}{ 0.001} \textbf{ L} \\[15pt]
= 0.0004 \textbf{ L} \)
Example 5
Convert \( 7 \; \color{red}{\textbf{centi}}\textbf{grams} \) to grams
Solution to Example 5
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt]
\color{red}{\textbf{ centi = }
0.01 = 1 \div 100 \\ \qquad \qquad = \displaystyle \frac{1}{100} = 10^{-2} } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ c }} \text {for centi and the sysmbol} \textbf{ g } \text {for grams to write } \\[15pt]
7 \; \color{red}{\textbf{centi}}\textbf{grams} \\[15pt]
= 7 \; \color{red} {\textbf{c}}\textbf{g} \\[15pt]
\text {Substitute } \color{red}{\textbf{c (centi) }} \text{ by its factor and evaluate} \\[15pt]
= 7 \times \color{red}{0.01} \textbf{ g} \\[15pt]
= 0.07 \textbf{ g} \)
Example 6
Convert \( 2.01 \; \color{red}{\textbf{deci}}\textbf{meters} \) to meters.
Solution to Example 6
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt]
\color{red}{\textbf{ deci = }
0.1 = 1 \div 10 \\ \qquad \qquad = \displaystyle \frac{1}{10} = 10^{-1} } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ d }} \text {for deci and the sysmbol} \textbf{ m } \text {for meters to write } \\[15pt]
2.01 \; \color{red}{\textbf{deci}}\textbf{meters} \\[15pt]
= 2.01 \; \color{red} {\textbf{d}} \textbf{m} \\[15pt]
\text {Substitute } \color{red}{\textbf{d (deci) }} \text{ by its factor and evaluate} \\[15pt]
= 2.01 \times \color{red}{0.1} \textbf{ m} \\[15pt]
= 0.201 \textbf{ m} \)
Example 7
Convert \( 5 \; \color{red}{\textbf{deka}}\textbf{meters} \) to meters.
Solution to Example 7
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ deka = }
10 } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ da }} \text {for deka and the sysmbol} \textbf{ m } \text {for meters to write } \\[15pt]
5 \; \color{red}{\textbf{deka}}\textbf{meters} \\[15pt]
= 5 \color{red}{\textbf{ da}}\textbf{m} \\[15pt]
\text {Substitute } \color{red}{\textbf{da (deka) }} \text{ by its factor and evaluate} \\[15pt]
= {5 \times \color{red}{10} \textbf{ m}} \\[15pt]
= 50 \textbf{ m} \)
Example 8
Convert \( 9.23 \; \color{red}{\textbf{hecto}}\textbf{liters} \) to liters.
Solution to Example 8
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ hecto = }
100 = 10^2 } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ h }} \text {for hecto and the sysmbol} \textbf{ L } \text {for liters to write } \\[15pt]
9.23 \; \color{red}{\textbf{hecto}}\textbf{liters} \\[15pt]
= 9.23 \; \color{red} {\textbf{h}} \textbf{L} \\[15pt]
\text {Substitute } \color{red}{\textbf{h (hecto) }} \text{ by its factor and evaluate} \\[15pt]
= {9.23 \times \color{red}{100} \textbf{ l}} \\[15pt] = 923 \textbf{ L} \)
Example 9
Convert \( 3.4 \; \color{red}{\textbf{kilo}}\textbf{grams} \) to grams.
Solution to Example 9
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ kilo = }
1000 = 10^3 } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ k }} \text {for kilo and the sysmbol} \textbf{ g } \text {for grams to write } \\[15pt]
3.4 \; \color{red}{\textbf{kilo}}\textbf{grams} \\[15pt]
= 3.4 \; \color{red} {\textbf{k}} \textbf{g} \\[15pt]
\text {Substitute } \color{red}{\textbf{k (kilo) }} \text{ by its factor and evaluate} \\[15pt]
= 3.4 \times \color{red}{1000} \textbf{ g} \\[15pt]
= 3400 \textbf{ g} \)
Example 10
Convert \( 7.6 \color{red}{\textbf{ Mega}}\textbf{Watts} \) to Watts.
Solution to Example 10
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ Mega = }
1000000 = 10^6 } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ M }} \text {for Mega and the sysmbol} \textbf{ W } \text {for Watts to write } \\[15pt]
7.6 \color{red}{\textbf{ Mega}}\textbf{Watts} \\[15pt]
= 7.6 \color{red}{\textbf{ M}} \textbf{W} \\[15pt]
\text {Substitute } \color{red}{\textbf{M (Mega) }} \text{ by its factor and evaluate} \\[15pt]
= {7.6 \; \times \color{red}{1000000} \textbf{ W}} \\[15pt]
= 7600000 \textbf{ W} \)
Example 11
Convert \( 0.3 \; \color{red}{\textbf{Giga}}\textbf{Watts} \) to Watts.
Solution to Example 11
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ Giga = }
1000000000 = 10^9 } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ G }} \text {for Giga and the sysmbol} \textbf{ W } \text {for Watts to write } \\[15pt]
0.3 \; \color{red}{\textbf{Giga}}\textbf{Watts}
\\[15pt] = 0.3 \; \color{red} {\textbf{G}}\textbf{W} \\[15pt]
\text {Substitute } \color{red}{\textbf{G (Giga) }} \text{ by its factor and evaluate} \\[15pt]
= {0.3 \times \color{red}{1000000000} \textbf{ W}} \\[15pt]
= 300000000\textbf{ W} \\ \)
Example 12
Convert \( 1.3 \; \color{red}{\textbf{Tera}}\textbf{Watts} \) to Watts.
Solution to Example 12
\( \text{Using the table above, the factor corresponding to the prefix} \\[15pt] \color{red}{\textbf{ Tera = }
1000000000000 = 10^{12} } \\[15pt]
\text {Use the symbol} \color{red}{\textbf{ T }} \text {for Tera and the sysmbol} \textbf{ W } \text {for Watts to write } \\[15pt]
1.3 \; \color{red}{\textbf{Tera}}\textbf{Watts} \\[15pt]
= 1.3 \; \color{red}{\textbf{T}}\textbf{W} \\[15pt]
\text {Substitute } \color{red}{\textbf{G (Giga) }} \text{ by its factor and evaluate} \\[15pt]
= {1.3 \times \color{red}{1000000000000} \textbf{ W}} \\[15pt]
= 1300000000000\textbf{ W} \\ \)
Exercises
Part A
Identify the prefix used and convert to meters (m).
\( \quad 0.02 \text { Mm}\)
\( \quad 234 \text { dam}\)
\( \quad 1200 \text { pm}\)
\( \quad 205 \text { nm} \)
\( \quad 0.002 \text { cm} \)
\( \quad 1.002 \text { hm} \)
\( \quad 0.005 \text { Gm} \)
\( \quad 1.34 \; \mu \text{m} \)
\( \quad 23000 \; \text{mm} \)
\( \quad 1.003 \; \text{dm} \)
\( \quad 0.02 \; \text{km} \)
\( \quad 0.01 \text { Tm} \)
Part B
Identify the prefix used and convert to grams (g).
\( \quad 0.003 \text { Tg} \)
\( \quad 0.3 \; \text{dg} \)
\( \quad 1.2 \; \text{kg} \)
\( \quad 1000 \; \mu \text{g} \)
\( \quad 0.056 \text { Mg}\)
\( \quad 2.3 \text { dag}\)
\( \quad 102.4 \text { cg} \)
\( \quad 20.2 \text { hg} \)
\( \quad 0.001 \text { Gg} \)
\( \quad 1100 \text { pg}\)
\( \quad 9000 \text { ng} \)
\( \quad 23000 \; \text{mg} \)
Part C
Identify the prefix used and convert to litters (L).
