Respuesta :
We will investigate how to express percentages as decimals ( fractions ). Then we will see how to manipulate these percentages to get the starting or resltant value.
We are asked to determine the " starting number " whose 0.2% would result in the final number:
[tex]22[/tex]We will first see how to deal with the percentage ( 0.2% ) and the starting number which is an unknown. So lets suppose:
[tex]\text{Starting number = x}[/tex]Then we will see how to deal with percentages. The way we deal is by using a basic mathematical operator of ( multiplication ) and convert the percentage into a fraction as follows:
[tex]\begin{gathered} \text{Starting number }\cdot\text{ Percentage} \\ x\cdot\frac{0.2}{100} \end{gathered}[/tex]Then we will equate the above expression to the resultant as follows:
[tex]x\cdot\frac{0.2}{100}\text{ = 22}[/tex]Now we have aa full fledged equation. We can easily manipulate and solve for the unknown number ( x ) as follows:
[tex]\begin{gathered} x\cdot0.2\text{ = 2200} \\ x\text{ = }\frac{2200}{0.2} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 11,000}} \end{gathered}[/tex]We see the unknown starting number ( x ) is very large as should have been the case. This is due to the fact that ( 0.2% ) is a very small proportion of a number such that it results in a two-digit number like ( 22 ). If the percentage is low but resultant is high, then the starting number must be very large!
Answer:
[tex]\textcolor{#FF7968}{11,000}[/tex]