Question

How do you convert $0.198$ to a fraction?

Answer 1

Hint: We first count the number of digits after the decimal point. The number of these digits denote the power of $10$ which is $3$ in this case. Now, we remove the decimal point and replace it with $\dfrac{1}{1000}$. After that, we reduce the fraction to its simplest form.

Complete step by step solution:
Fractions are a way to define divisions. For example, $\dfrac{1}{2}$ means division of $1$ by $2$. The number above the bar is called the numerator and the number below it is called denominator. Fractions are of various types like, proper fraction (where the numerator is smaller than the denominator), improper fraction (where the denominator is smaller than the numerator), and so on. Decimals also represent divisions, but consider the divisions to be divided by multiples of $10$. Decimals also denote the same thing but in a different format; in place of bar, it uses a point with numbers lying on the left and right sides of it.
Decimal to fraction conversion or fraction to decimal conversion is very easy. In decimals, we count the number of digits after the decimal point. The number of digits denotes the power of $10$ which divided the original number and transformed it to a decimal. In this problem, we are given the number as $0.198$. The number of digits after the decimal point are $3$. So, the power of $10$ will be $3$. That means, if we want to remove the decimal point, we have to replace it with “division by ${{10}^{3}}$“. The decimal thus becomes,
$0.198=\dfrac{198}{1000}$
We can see that the fraction is not in its reduced form. So, we divide the numerator and denominator by $2$ to get,
\[\dfrac{\dfrac{198}{2}}{\dfrac{1000}{2}}=\dfrac{99}{500}\]
Therefore, we can conclude that the fraction will be \[\dfrac{99}{500}\].

Note: In these conversions, we should count the number of digits after the decimal point correctly as doing it incorrectly gives wrong results. Also, we should check if the fraction that we get after replacing the decimal point with $10$ or its multiples is in its simplest form or not.