Question

How do you find the reciprocal of 2.5?

Answer 1

Hint: In this question, we are given a decimal and we have to find its reciprocal. To do so, we will first convert the decimal into a fraction. A fraction is defined as a combination of two integers that are separated by a horizontal line, the term on the upper side of the horizontal line is called the numerator and the term on the lower side of the horizontal line is called the denominator. To find the reciprocal of a fraction, we switch the positions of the numerator and the denominator with each other, that is, we write the numerator at the place of the denominator and the denominator at the place of the numerator. For example, let a fraction be \[\dfrac{x}{y}\] then the reciprocal of this fraction is $\dfrac{y}{x}$.

Complete step by step answer:
The 2.5 can be written in the fraction form as –
$ \Rightarrow 2.5 = \dfrac{{25}}{{10}}$
Now the reciprocal of this fraction is equal to $\dfrac{{10}}{{25}}$ .
This fraction can be further simplified as –
$
\Rightarrow \dfrac{{10}}{{25}} = \dfrac{{2 \times 5}}{{5 \times 5}} \\
   \Rightarrow \dfrac{{10}}{{25}} = \dfrac{2}{5} \\
 $
Hence, the reciprocal of 2.5 is equal to $\dfrac{{10}}{{25}}$ or $\dfrac{2}{5}$ .

Note: For converting a decimal into the fraction form, we multiply and divide the decimal with 10 raised to some power such that the power is equal to the number of digits at the right side of the decimal as in this question we multiplied and divided the decimal by 10 raised to power 1. The reciprocal of a fraction is also known as its multiplicative inverse because when it is multiplied with the original fraction, we get 1 as the answer.