Question

How do you write 0.76 as a fraction in lowest terms?

Answer 1

Hint: In this question, we are given a decimal expression and we have to convert it into a fraction in the lowest terms, that is, we have to first convert the decimal into a fraction and then simplify the obtained fraction. A decimal can be converted into a fraction by multiplying and dividing the decimal with 10 raised to the power that is equal to the number of digits on the right side of the decimal point. For example, 0.01 is a decimal number, to convert it into a fraction we will multiply and divide it by ${10}^2$

Complete step-by-step solution:
We have to convert 0.76 into a fraction. There are 2 digits on the right side of the decimal so we multiply and divide the given number by ${10}^2$ , so we get –
$$\begin{gathered} 0.76=0.76\times {\displaystyle \frac{{10}^2}{{10}^2}} \\ \Rightarrow 0.76={\displaystyle \frac{76}{100}} \end{gathered}$$
Thus, the decimal is converted into fraction form. Now we will simplify the above fraction by canceling out the common factors –
$$\begin{gathered} \Rightarrow 0.76={\displaystyle \frac{76}{100}}={\displaystyle \frac{4\times 19}{4\times 25}} \\ \Rightarrow 0.76={\displaystyle \frac{19}{25}} \end{gathered}$$
Hence 0.76 as a fraction in lowest terms is ${\displaystyle \frac{19}{25}}$ .

Note: A fraction is simplified by expressing the numerator and the denominator as a product of its prime factors and then canceling out the common factors. When the value of the numerator is greater than that of the denominator, the term on the left side of the decimal is greater than zero and if the value of the denominator is greater than that of the numerator, the digit on the left side of the decimal is zero. There can be infinite decimals that are equivalent to the given decimal.