Table 3 summarizes the most common units in use. In the first column there is a prefix written, in the second column these prefixes are together with the metre of the basic unit of length. In the third column, the prefixes are connected to the unit of volume by a cubic meter and, in the fourth colloquial language, to the more common unit of volume. The last two columns describe what to do when moving up or down. If the centimetres are to be converted to millimetres, i.e. moved upwards, then the number is multiplied by the number 10 mentioned in the top row. This factor is always used when moving[b] one[/b] line up or down. If you want to convert centimetres into decimeters, then the number is divided by 10.

The basic units are described in Table 1 of the SI system. For example, the basic unit of length is metre and kilogram of mass. These are the units used in the calculation. In colloquial language, it is more common to use multiples of these. For example, the length of the driven distance is preferred to be described in kilometers and the weight of the spider in grams. Another example is that a cardboard strawberry box is designed with length measures. In this case, its volume is obtained in cubic meters. However, in practice, volume is described in liters.[br][br]Prefix of a unit express its magnitude compared to a basic unit. For example,[br][br]  [math]\Large 1\text{ km} = 1\cdot 10^3\text{ m}=1000 \text{ m}\\[br]\Large 1\text{ cm}=1\cdot 10^{-2}\text{ m}=0.01\text{ m}[/math][br][br] [br]If volume is solved with units of length but the context requires solution in litres, transformation can be done with [br][br]  [math]\LARGE \textcolor{blue}{1\text{ l}=1\text{ dm}^3.}[/math] [br][br]

The latest column in Table 4 can be used for multiple unit transformations. It is known to all that one meter is 100 centimetres. Let's use this to understand the idea. Since the meter is a basic unit, then it is in the "empty" line in the center of the table. This row in the last column contains 10[sup]0[/sup]. For a cent, the corresponding number is 10[sup]-2[/sup].[br] [br]The transformation formula could be written as follows, utilizing the potentials:[br] [br][math]\Large 10^{\textcolor{blue}{\text{what}}-\textcolor{purple}{\text{to where}}} .[/math][br] [br]For example, 1 meter is converted to centimetres:[br] [br]  [math] \Large 1\text{ m}=1\cdot 10^{\textcolor{blue}{0}-(\textcolor{purple}{-2})}\text{ cm}=1\cdot 10^2\text{ cm}=100\text{ cm}.[/math][br] [br]The same idea works in more difficult cases. See the examples below.

[u]Lengths:[/u][br][br][math]\Large 2.3\text{ cm}=2.3\cdot 10^{-2-0}\text{ m}=2.3\cdot 0.01 \text{ m}=0.023 \text{ m}\\[br]\Large 0.5\text{ km}=0.5\cdot 10^{3-(-1)}\text{ dm}=0.5\cdot 10^4 \text{ dm}=5000 \text{ dm}[/math][br][br][u]Area:[/u][br][br][math]\Large 1\text{ m}^2=1\cdot (10^{0-(-2)}\text{ cm})^2=1\cdot (10^2)^2\text{ cm}^2=10^4\text{ cm}^2=10000\text{ cm}^2\\[br]\Large 0.01\text{ ha}=0.01\cdot (10^{2-0}\text{ m})^2=0.01\cdot 10^4 \text{ m}^2=1\cdot 10^2 \text{ m}^2=100\text{ m}^2\\[br]\Large 4.7\text{ dm}^2=4.7\cdot (10^{-1-(-2)}\text{ cm})^2=4.7\cdot 10^2 \text{ cm}^2=470\text{ cm}^2[/math][br][br][u]Volume:[/u][br][br][math]\Large 1\text{ m}^3=1\cdot (10^{0-(-1)}\text{ dm})^3=1\cdot (10^1)^3\text{ dm}^3=10^3\text{ dm}^3=1000\text{ dm}^3=1\text{ }\cal l\\[br]\Large 2\text{ }\cal l=2 \text{ dm}^3=2\cdot (10^{0-1}\text{ m})^3=2\cdot 10^{-3} \text{ m}^3=2\cdot 0.001\text{ m}^3=0.002\text{ m}^3\\[br]\Large 5.2\text{ dl}=5.2\cdot 10^{-1-(-3)}\text{ ml}=5.2\cdot 10^2 \text{ ml}=520\text{ ml}\\[br]\Large 3.1\text{ dl}=0.31 \text{ }\cal l=0.31 \text{ dm}^3=0.31\cdot 1000 \text{ cm}^3=310\text{ cm}^3[br][br][/math]

[color=#0000ff]Example 2[/color]. Wind speed is informed to be 18 m/s. What speed of a car does it correspond?[br][br]Speed of a car is usually given as km/h. Let us transform the given wind speed to this unit:[br][br]  [math]\Large 18 \text{ m/s} = 18 \frac{10^{-3}\text{ km} }{\frac{1}{60\cdot 60}\text{ h}}=18\cdot \frac{3600}{10^3} \text{ km/h}\approx 64.8 \text{km/h}.[/math][br][br][br][br][color=#0000ff]Example 3[/color]. It is noticed, that there is dropping water from a pipe with a speed of 60 litres in two hours. Calculation need units in SI system, so let us transform it to m[sup]3[/sup]/s.   [br][br]  [math]\Large \frac{60\text{ l}}{2\text{ h}}= \frac{60\text{ dm}^3}{2\cdot 60\cdot 60\text{ s}}=\frac{(10^{-1})^3\text{ m}^3}{2\cdot 60 \text{ s}}\approx 8.3\cdot 10^{-6}\text{ m}^3\text{/s}.[/math][br] [br][br]

[color=#0000ff]Example 4. [/color]Timo took off at 8:31 and arrived at 13:28. How long did it take?[br] [br]As the hour is borrowed, 60 min is added to 28 min: 60min+28min =88min. Then the subtraction is calculated, i.e. 88min-31 min= 57 min.[br] [br][math]\large\begin{array}{crcll}[br]&\cancel{13}^{12}&:&\cancel{28}^{88}\\[br]-& 8&:&31\\[br]\hline[br]& 4&:&57[br] [br]\end{array}[/math][br] [br]If your calculator has the [math]\large ^\circ '\,''[/math] key, then you can calculate the time directly on it. Type the times:13 "key" 28 "key" minus sign 8 "key" 31 "key" equals sign. Now the screen should have [math]\large 4^\circ 57' 0''.[/math].[br] [br]NOTE! Not all calculators have that key.[br][br][br][br][br]