Question

What is 210 mm in cm?

Answer 1

Hint: We first explain the relation between the two units of distance given which are cm and mm. We can see that the relation between them can be represented as $10mm=1cm.$ Using this, we convert the given value in question 210 mm which is in millimetres to centimetres using the above relation and represent the final answer in terms of centimetre.

Complete step-by-step solution:
To solve this question, we need to show the relation between the two units first. Let us represent them in terms of the standard unit of length metre. Using these let us then show the relationship between cm and mm.
We know 1 metre can be represented in terms of centimetre as,
$\Rightarrow 1m=100cm$
This is because the word ‘centi’ means hundred. Therefore, one metre is equal to 100 centimetres.
Now we know the relation between metre and millimetre can be given by,
$\Rightarrow 1m=1000mm$
Here, the word ‘milli’ represents one thousand. Equating the right-hand sides of both the above equations, we can obtain the relation between the units cm and mm.
$\Rightarrow 100cm=1000mm$
Dividing both sides of the equation by 1000,
$\Rightarrow {\displaystyle \frac{1}{10}}cm=1mm$
Now, we need to convert the given value 210 mm to cm. To do this, we know 1 mm is ${\displaystyle \frac{1}{10}}cm,$ therefore, 210 mm will be equal to,
$\Rightarrow 210mm=210\times {\displaystyle \frac{1}{10}}cm$
Dividing the two terms on the right-hand side, we get
$\Rightarrow 210mm=21cm$
Hence, 210 mm in cm is expressed as $21cm.$

Note: It is important to know the basic units and their conversions. Many times, we need to convert from one unit to another in order to modify the units according to our needs. To do so, we must know the topic of unit conversion. We can also solve this question by first converting 210 cm to metres and then converting from metres to mm. This involves 2 steps of calculation but provides the same results.