Question

Express $0.245$ as a fraction in the simplest form.

Answer 1

Hint: As we know that a fraction is a mathematical expression that consists of a numerator and a denominator, here the denominator refers to the total number of parts in a whole. While on the other hand, the numerator refers to the number of parts in question from the whole. fraction can also be used to represent ratios and divisions as well. It is shown in the form of $\dfrac{a}{b}$, where $a$ is the numerator of the fraction and $b$ represents the denominator of the fraction. While we can define a decimal number as a number whose whole number part and fractional part is separated by a point and that point or dot is called a decimal point.

Complete step by step answer:
Here the given number is $0.245$. First we will convert it into the form of fraction as i.e. $\dfrac{{245}}{{1000}}$.
Since we know that a fraction is in simplest form only when its numerator and the denominator are relatively prime which means that they have no common factors other than $1$. We can say it as in its lowest term.
So we will write the fraction in the form of their factors $\dfrac{{245}}{{1000}} = \dfrac{{5 \times 49}}{{10 \times 10 \times 5 \times 2}}$.
It gives us the value $\dfrac{{49}}{{200}}$.

Hence the simplest form of $0.245$ is $\dfrac{{49}}{{200}}$.

Note: We should also note that it is the simplest form of fraction with the given numerator and the denominator as there is no multiple common between numerator and the denominator, so it cannot be simplified further. But it can be written in decimal and the decimal form of the fraction $\dfrac{{49}}{{200}}$ is again the same value $0.245$. We should also know that a fraction that has $1$ in the denominator is called a Unit fraction, since they represent the whole number itself, without any further divisions. Also a fraction cannot have $0$ as its denominator as then the value of such fraction would be only undefined or infinity i.e. $\infty $.