Question

Express the ratio expression in simplest form: 1 century to 1 decade.

Answer 1

Hint: When we find the ratio between two different units then convert the bigger unit into smaller units. Ratio of any expression is only carried when units are the same. After converting the units simplify the expression unit it becomes indivisible.

Complete step-by-step answer:
The given expression for the simplification is: 1 century to 1 decade.
First writing the given expression in $ \dfrac{p}{q} $ form so we get,
 $ \dfrac{{1\;{\rm{century}}}}{{1\;{\rm{decade}}}} $
Now we will convert the century into the decade as century is the bigger unit of time then decade.
As we know that, there are 10 decades in one century so,
 $ \Rightarrow {\rm{1}}\;{\rm{Century = 10}}\;{\rm{Decades}} $
Writing the value of 1 century then we get,
 $ \Rightarrow \dfrac{{10\;{\rm{Decades}}}}{{1\;{\rm{decades}}}} $
Now, we can easily cancel out the same quantities then we get,
 $ \Rightarrow \dfrac{{10\;}}{1} $
Here, we will get the fraction form so, solving this fraction form till it didn’t become indivisible but $ \dfrac{{10\;}}{1} $ is already indivisible
Here, 10 and 1 are never divided by the same number hence it is the simplest form.
Hence the simplest form of the given expression (1 century to 1 decade) is $ \dfrac{{10\;}}{1} $ .

Note: In this type of question, convert the bigger unit into smaller units. When we convert the bigger unit into a smaller unit then the number of smaller units present in one bigger unit is multiplied with the bigger unit and when we convert the smaller unit into a bigger unit then the number of smaller units present in one bigger unit divides the smaller unit. To get the ratio of any expression it is compulsory to make the units similar.