Question

How do you convert $7.8{\text{km}}$ to ${\text{miles}}$?

Answer 1

Hint: In this type of problem, where we need to convert one unit to another, we must know what the conversion factor should be for that conversion from one unit to another. So we must know that $5{\text{ miles}} = 8{\text{km}}$ and accordingly we can apply the unitary method and find what $7.8{\text{km}}$ equals to.

Complete step by step solution:
Here we are given to convert $7.8{\text{km}}$ to ${\text{miles}}$.
So in order to convert from one unit to another we must know that $5{\text{ miles}} = 8{\text{km}}$.
This information is to be known as without this we cannot solve the above problem. This can be made clearer with an example: If we require to convert ${\text{meter to centimeter}}$ we must know that ${\text{1 meter}} = 100{\text{ centimeter}}$.
Also if we have weight in kilogram and we need to convert in grams we need to know that:
${\text{1 kilogram}} = {\text{1000 grams}}$
Similarly for the above problem, we must know the conversion that:
$5{\text{ miles}} = 8{\text{km}}$
From this we can say that:
${\text{1 miles}} = \dfrac{8}{5}{\text{km}}$
Now we need to find what one kilometer will be equal to in miles because in the problem we are given in the kilometer and we need to convert it into miles. So we must know what one kilometer is equal to in miles.
So we can say that:
${\text{1 miles}} = \dfrac{8}{5}{\text{km}}$
${\text{1km}} = \dfrac{5}{8}{\text{miles}}$
Now we know that if we have the price of one item and we need to find the price of $n$ items, we just need to multiply that price of one item with $n$.
Similarly, we need to multiply the equation (1) with $7.8$ to get the value of $7.8{\text{km}}$in miles.
${\text{1km}} = \dfrac{5}{8}{\text{miles}}$.
${\text{7}}{\text{.8km}} = \dfrac{5}{8} \times {\text{7}}{\text{.8miles}} = (0.625)(7.8) = 4.875{\text{ miles}}$.

So we can say that:
$7.8{\text{km}} = 4.875{\text{ miles}}$

Note: Here the student must only need to remember the conversion factors of how many parts of one unit makes the other unit and then he must know the unitary method to convert accordingly into the required unit.