Question

How do you write $0.1$ as a decimal and a fraction?

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 number is $0.1$. We can see here that the whole number part $0$ and the fractional part $1$ is separated by a dot, known as the decimal point. Hence $0.1$ is already in the decimal form.
Now to convert it into a fraction, we will divide $0.1$ by $1$.
$ \Rightarrow \dfrac{{0.1}}{1}$
Since there is only one digit after the decimal point, we multiply both the numerator and denominator by $10$.
$ \Rightarrow \dfrac{{0.1 \times 10}}{{1 \times 10}}$
$ \Rightarrow \dfrac{1}{{10}}$

Hence $0.1$ can be written in a fractional form as $\dfrac{1}{{10}}$.

Note: Not all decimals can be converted to fraction 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.