Question

What is the expression of 0.23 in terms of vulgar fraction (a fraction expressed by a numerator and denominator)?
$$\begin{gathered} \text{A}\text{. }{\displaystyle \frac{7}{30}} \\ \text{B}\text{. }{\displaystyle \frac{23}{100}} \\ \text{C}\text{. }{\displaystyle \frac{23}{90}} \\ \text{D}\text{. }{\displaystyle \frac{7}{90}} \end{gathered}$$

Answer 1

Hint- Here, we will proceed by using the simple concept of multiplying the numerator and denominator of the given number (in decimal form) by ${10}^n$ where n denotes the number of digits occurring after the decimal point provided the last digit is non-zero.

Complete step-by-step answer:
Vulgar fraction is a fraction which consists of a numerator and a denominator where the denominator can never be equal to zero because if the denominator becomes zero then the fraction will not be defined.
The given number 0.23 is in the form of a decimal number and we can convert any decimal number by simply counting the number of digits which occur after the decimal point provided the last digit is non-zero and then multiplying both the numerator and the denominator of the decimal number by ${10}^n$ where n denotes the number of digits occurring after the decimal point provided the last digit is non-zero.
Here, 0.23 consists of 2 digits after the decimal point and the last digit is non-zero so this result is valid. Now, we will multiply the numerator and denominator of the number 0.23 by ${10}^n={10}^2=100$.
0.23 = ${\displaystyle \frac{0.23}{1}}={\displaystyle \frac{0.23\times 100}{1\times 100}}={\displaystyle \frac{23}{100}}$
Therefore, ${\displaystyle \frac{23}{100}}$ is the required expression of 0.23 in terms of vulgar fraction.
Hence, option B is correct.

Note- In this particular problem, the given number in decimal form is 0.23 which doesn’t contain any zero digit at the end. Let us suppose we have to express the number 0.70 in terms of vulgar fraction, here we will multiply the numerator and the denominator by ${10}^{n-x}$ where n denotes the number of digits occurring after the decimal point provided the last digit is non-zero and x denotes the total number of zero digits occurring consecutively at the end of the decimal number (in case of 0.70, n = 2 and x = 1 so we will get ${\displaystyle \frac{7}{10}}$).