Question

What is 17.5% as a fraction?

Answer 1

Hint: The percentage x can be written as \[\dfrac{x}{100}\]. Now we have to find the simplest form of \[\dfrac{x}{100}\] to have a fraction which is given in the form of percentage. By using this concept, this problem can be solved.

Complete step-by-step solution:
From the question, we were given that we have to convert 17.5% as a fraction.
Let us assume the value of x is equal to 17.5%.
\[\Rightarrow x=17.5%\]
Let us assume this as equation (1).
\[\Rightarrow x=17.5%.....(1)\]
We know that the percentage x can be written as \[\dfrac{x}{100}\]. Now we have to find the simplest form of \[\dfrac{x}{100}\] to have a fraction which is given in the form of percentage.
So, we have to apply this concept for equation (1), then we get
\[\Rightarrow x=\dfrac{17.5}{100}\]
Let us assume this as equation (2).
\[\Rightarrow x=\dfrac{17.5}{100}.....(2)\]
We know that \[x.y\] can be written as \[xy\times {{10}^{-1}}\].
So, we have to apply this concept for equation (2), then we get
\[\Rightarrow x=\dfrac{\dfrac{175}{10}}{100}=\dfrac{175}{1000}\]
Let us assume this as equation (3).
\[\Rightarrow x=\dfrac{175}{1000}.....(3)\]
Now we have to convert the fraction obtained in equation (3) into simplest form, then we get
\[\Rightarrow x=\dfrac{7}{40}\]
Now let us assume this as equation (4).
\[\Rightarrow x=\dfrac{7}{40}.....(4)\]
From equation (4), it is clear that the value of x is equal to \[\dfrac{7}{40}\].
So, it is clear that \[\dfrac{7}{40}\]is the fractional form of 17.5%.

Note: Students may undergo calculation mistakes while solving this problem. If a small mistake is done, then the final answer may get interrupted. So, these mistakes should be avoided while solving the problem. Students should follow a correct calculation procedure.