Question

What is the ratio of 1 mm to 1 cm?
(a) 1 : 100
(b) 10 : 1
(c) 1 : 10
(d) 100 : 1

Answer 1

Hint: We know how a metre (m) is related to centimetres (cm) and millimetres (mm). These relations are 1 m = 100 cm and 1 m = 1000 mm. Using these two relationships, we can find the relation between centimetres and millimetres. And thus, we can find the ratio among them.

Complete step by step solution:
We know very well that centimetre (cm) and millimetre (mm) are units of length.
Also, we know that the relationship between a metre and a centimetre is
1 m = 100 cm …(i)
and, the relationship between a metre and a millimetre is
1 m = 1000 mm …(ii)
The LHS of both equation (i) and equation (ii) are the same. Thus, the RHS of both equations must also be equal. Hence, we can write
100 cm = 1000 mm
We can simplify this to get
1 cm = 10 mm …(iii)
Now, in our question, we need to find the ratio of 1 mm to 1 cm. Thus, the required ratio is,
$Ratio={\displaystyle \frac{1\text{ mm}}{1\text{ cm}}}$
We can now substitute the value of 1 cm from equation (iii) to get
$Ratio={\displaystyle \frac{1\text{ mm}}{10\text{ mm}}}$
$\Rightarrow Ratio={\displaystyle \frac{1}{10}}$
Thus, we find that the ratio of 1 mm to 1 cm is 1 : 10 .

So, the correct answer is “Option C”.

Note: We must be very clear that a ratio a : b can be expressed as ${\displaystyle \frac{a}{b}}$ in fraction, and both of them are used interchangeably. So, we must not confuse between the two. We must also take care that we have to find the ratio of 1 mm to 1 cm, i.e., 1 mm : 1 cm, and not vice versa.