Finding ratio by changing units

Suppose I have two cats

So, Ratio of length of cat to baby cat = 20/10

= 2/1

= 2 : 1

So, cat is twice as long as baby cat

Now, let’s take

So, Ratio of length of the cat to the Lion = 20/2

= 10/1

= 10 : 1

So, cat is 10 times as long as Lion?

WRONG

Here units are different

Cat’s length is in cm

Lion’s length is in m

So, we convert cm to m or cm

So,

Cat’s length = 20 cm

Lion’s length = 2 m

     = 2 × 100 cm

     = 200 cm

So, Ratio of cat’s length to lion’s length = 20/200

 = 1/10

 = 1 : 10

So, Cat’s length is 1/10 th of lion’s

So, we have to keep in mind units when forming ratio