Measuring Length

$\underline{Metric\ System\ Units\ For\ Length}$

The basic unit of mass in metric system is $meter$ written in short form as $m$

The other commonly used units in metric system are:

$Kilometer = Meter \div 1000$

$Hectometer = Meter \div 100$

$Dekameter = Meter \div 10$

$Decimeter = Meter \times 10$

$Centimeter = Meter \times 100$

$Milligram = Meter \times 1000$

The conversion table for $Meter$ to various other units is as follows:

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	$(mm)$	$(cm)$	$(dm)$	$(m)$	$(dam)$	$(hm)$	$(km)$
$Millimeter\ (mm)$	$1$	$\div 10$	$\div 100$	$\div 1000$	$\div 10000$	$\div 100000$	$\div 1000000$
$Centimeter\ (cm)$	$\times 10$	$1$	$\div 10$	$\div 100$	$\div 1000$	$\div 10000$	$\div 100000$
$Decimeter\ (dm)$	$\times 100$	$\times 10$	$1$	$\div 10$	$\div 100$	$\div 1000$	$\div 10000$
$Meter\ (m)$	$\times 1000$	$\times 100$	$\times 10$	$1$	$\div 10$	$\div 100$	$\div 1000$
$Dekameter\ (dam)$	$\times 10000$	$\times 1000$	$\times 100$	$\times 10$	$1$	$\div 10$	$\div 100$
$Hectometer\ (hm)$	$\times 100000$	$\times 10000$	$\times 1000$	$\times 100$	$\times 10$	$1$	$\div 10$
$Kilometer\ (km)$	$\times 1000000$	$\times 100000$	$\times 10000$	$\times 1000$	$\times 100$	$\times 10$	$1$

How to use this table? Suppose you are to convert some value from the unit $dam$ to $cm$. You should select the row starting with $Dekameter$, and within that row select the cell corresponding to the column $cm$. The cell says $\times 1000$. Therefore, you need to multiply your $dam$ value with $1000$ to get the corresponding $cm$ value.

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$\underline{Adding\ Or\ Subtracting\ Length\ Values}$

When length values are expressed using mixed units, for example $3\ m\ 35\ cm$ and $2\ m\ 75\ cm$, we can add or subtract them by:

1. Converting them to a single unit, or by,

2. Adding the appropriate units separately.

We can write:

$3\ m\ 35\ cm + 2\ m\ 75\ cm$

$= 335\ cm + 275\ cm$

$= 610\ cm$

$= 6\ m\ 10\ cm$

Or, we can also solve it the following way:

$3\ m\ 35\ cm + 2\ m\ 75\ cm$

$= 3\ m + 35\ cm + 2\ m + 75\ cm$

$= 5\ m + 110\ cm$

$= 5\ m + 1\ m + 10\ cm$

$= 6\ m\ 10\ cm$

Similarly subtraction can be done in both the ways. But to avoid carry over errors you are advised to use the first method, which involves converting both values to the lowest unit required.