Question

How do you express $0.33$ as a fraction in the simplest form?

Answer 1

Hint: Decimal is a number whose whole number part and fractional part is separated by a point known as a decimal point. Whereas, the fraction is defined as equal parts of a whole. When we divide a collection or whole into equal parts, each part is a fraction of the whole. Both fractions and decimals represent the relation of a part with the whole.
To convert a decimal into a fraction, we divide the decimal by $1$. We then multiply both the numerator and denominator by $10$ for every digit after the decimal point. And hence we get a fraction after simplifying.

Complete step by step solution:
The given decimal is $0.33$. To convert it into a fraction, we will divide $0.33$ by $1$.
$ \Rightarrow \dfrac{{0.33}}{1}$
Since there are two digits after the decimal point, we multiply both the numerator and denominator by $100$.
$ \Rightarrow \dfrac{{0.33 \times 100}}{{1 \times 100}}$
$ \Rightarrow \dfrac{{33}}{{100}}$
For simplifying the fraction in the simplest form, we will find the Greatest Common Divisor (GCD) of $33$ and $100$.
In order to find the GCD, we will have to find the factors of $33$ and $100$. Therefore
$33 = 3 \times 11 \times 1$
$100 = 2 \times 2 \times 5 \times 5 \times 1$
Since there are no common factors of $33$ and $100$ other than $1$, therefore
$GCD(33,100) = 1$
We will now divide both the numerator and denominator ($33$ and $100$) by $1$.
$ \Rightarrow \dfrac{{\dfrac{{33}}{1}}}{{\dfrac{{100}}{1}}} = \dfrac{{33}}{{100}}$

Hence $0.33$ can be written in a fractional form as $\dfrac{{33}}{{100}}$.

Note:
Not all decimals can be converted to fractions by the given method. One such type of decimals is the recurring decimals. A recurring decimal is a number that keeps repeating forever after the decimal point. To convert it into a fractional form, we will have to generate two equations that have the same repeating part and subtract one from the other to remove it.