What will be the ratio of 18 mm to 3 cm.

Hint: Convert the two terms into the same units before taking the ratio. The conversion factor to convert from cm to mm is 10 cm/mm. Use this to convert 3 cm to mm and then take the ratio.

Complete step-by-step answer:

A ratio is defined as the quantitative relation between the two amounts showing the number of times one value contains or is contained within the other. It can be either represented as fractional form or with the colon symbol ‘:’ separating the two numbers. The ratio is a division of similar quantities and hence does not have a unit.

Before we divide the numbers to find the ratio, we need to make sure that the numbers are in the same units.

In this problem, we need to find the ratio of 18 mm to 3 cm.

Observe that they are in two different units, one is in mm and the other one is in cm. Hence, we can not directly divide them to find the ratio.

Hence, we convert 3 cm into mm.

We know that the value of 1 cm is equal to 10 mm. Hence, the value of 3 cm is given as a product of 3 and 10 mm.

\[3cm = 3 \times 10mm\]

Simplifying, we have:

\[3cm = 30mm\]

Now, we can find the ratio of 18 mm to 30 mm as follows:

Ratio = \[\dfrac{{18mm}}{{30mm}}\]

The units cancel out and simplifying the expression, we get:

 Ratio = \[\dfrac{3}{5}\]

Hence, the required ratio is 3:5.


Note: You might make a mistake by directly dividing 18 by 3 to get the answer as 6: 1 but this answer is wrong. The quantities must be in the same units before we divide to find the ratio.