Question

If the earth is an average of $ 9.3\times {{10}^{7}} $ $ miles $ from the Sun, how far is this distance in $ kilometers $ ?

Answer 1

Hint: In order to solve this question we will need to recall and memorize the concept of length conversion and the need of different length units, then we will see how much does $ 9.3\times {{10}^{7}} $ $ miles $ is in $ kilometers $ and in $ meters $ as well.

Complete step by step answer:
As we know length is the term used for identifying the size of an object or distance from one point to another and there are various units of length used in our day to day life to define the distance or length. The length of any object is its extended dimension (its longest side). The standard unit of length based on the metric system is a $ meter\left( m \right) $ .
Let’s understand a few of the length units:
 A $ meter $ is defined as the distance covered by light in vacuum in $ \dfrac{1}{299,729,458} $ seconds.
 $ kilometer $ is a metric unit of measurement which is equal to 1,000 $ meters $ .
 $ Mile $ is a unit of distance that is equal to $ 1,760 $ $ yards $ or $ 1.6 $ $ kilometers $ .
 $ Yard $ is a unit of measurement that is equal to three $ feet $ or approximately $ 9.14 $ $ centimeters $ .
Now, why do we need various units of length? The answer is quite simple. One cannot measure the length of a pencil in $ kilometers $ or even in $ meters $ as it will be very complicated to do so, instead it should be measured in $ centimeters $ to maintain simplicity. In the same way one cannot measure height of a tree in $ centimeters $ as it will be very tedious and complex, rather it should be measured in $ meters $ or $ feet $ . So different units of length are required according to their need.
As we studied above, we know that $ 1mile $ equals $ 1.6kilometers $
 $ \therefore 9.3\times {{10}^{7}}miles=9.3\times {{10}^{7}}\times 1.6=14.88\times {{10}^{7}}kilometers $
 $ \Rightarrow 9.3\times {{10}^{7}}miles=14.88\times {{10}^{7}}\times {{10}^{-3}}=14.88\times {{10}^{4}}meters $
Hence, $ 14.88\times {{10}^{7}}kilometers $ is the required answer.

Note:
One must know the basic length conversions like conversion of meter into centimeters, kilometer, etc to solve these kind of length conversion based questions. Also be careful while doing the reverse calculation, such as $ kilometer $ to $ miles $ as it is to divide and not to multiply in the equation.