Question

Find the ratio of the following:
5 m to 10 km

Answer 1

Hint : To find the proper ratio, all units should be converted to SI unit system. One kilometre (1 km) is equal to one thousand metre (1000 m).

Complete step by step answer
As seen, two distances are given, and the ratio of one to the other is expected to be found.
Ratio, in general is the division of one value by another, usually of the same quantity. It is a measure of how one of the values is greater than the other or how much it is smaller. When we say, find the ratio of A to B, we mean find how large or how small A is relative to B. it is written in mathematical terms as A : B, which is read as A ratio B. For example, if a quantity A is twice as large as B, then the ratio of A to B would be written as $ A:B = 2:1 $ . It can be calculated as
 $ \dfrac{A}{B} = \dfrac{A}{{2A}} = \dfrac{1}{2} $ .
On the other hand, the ratio of B to A would be the other way around as in $ B:A = 1:2 $ . The quantities however, must be in the same unit.
Hence, to calculate the ratio of 5 m to 10 km, we convert 10 km into metres, which is
 $ 10km = 10000m $
Then
 $ \dfrac{5}{{10000}} = \dfrac{1}{{2000}} $ ,
And in ratio, $ 1:2000 $
Hence, the final answer is $ 1:2000 $ .

Note
Alternatively, we can convert the 5 m into km because it is not required for the system to be in SI, just required to be in the same unit system. Hence,
 $ 5m = 0.005km $
Then,
 $ \dfrac{{0.005}}{{10}} = \dfrac{1}{{2000}} $ .
We should note that ratios are written in whole numbers.