Question

What is 39.5% written as a fraction in simplest form?

Answer 1

Hint: To find the simplest form of 39.5% as a fraction, we have to convert 39.5% into its fractional form by dividing it by 100. Then, we have to change 39.5 from decimals to its number form by multiplying the result by ${\displaystyle \frac{10}{10}}$ . Then, we have to simplify.

Complete step by step solution:
We have to find the simplest form of 39.5% as a fraction. Firstly, we have to convert 39.5% into its fractional form by dividing it by 100.
$39.5\mathrm{\%}={\displaystyle \frac{39.5}{100}}$
Now, we have to change 39.5 in the numerator to its number form by removing the decimal. Since the decimal place contains only one digit, we will have to multiply 39.5 by 10. Therefore, we will multiply ${\displaystyle \frac{39.5}{100}}$ with ${\displaystyle \frac{10}{10}}$ .
$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{39.5}{100}}\times {\displaystyle \frac{10}{10}}\\ & ={\displaystyle \frac{395}{1000}}\end{array}$
Now, we have to simplify the above result by cancelling the common factor 5. The, the above result can be written as
$\Rightarrow {\displaystyle \frac{395}{1000}}={\displaystyle \frac{79}{200}}$
Therefore, 39.5% written as a fraction in simplest form is ${\displaystyle \frac{79}{200}}$.

Note: Students must know to convert percentages into its number form. They have a chance of making mistakes by considering ${\displaystyle \frac{39.5}{100}}$ as the simplest form. We can say that a fraction is in simplest form when the numerator and denominator cannot be any smaller, while still being whole numbers. We have multiplied ${\displaystyle \frac{39.5}{100}}$ by ${\displaystyle \frac{10}{10}}$ because the result of ${\displaystyle \frac{10}{10}}$ is 1 and we can write ${\displaystyle \frac{39.5}{100}}$ as ${\displaystyle \frac{39.5}{100}}\times 1$ . We used 10 instead of other numbers because the decimal place contains only one digit.