Question

22 is 0.2% of what number? Use pencil and paper. Would you expect the answer to be a lot less than22, slightly less than 22, slightly greater than 22, or a lot greater than 22? Explain.22 is 0.2% of |(Type an integer or a decimal.)

Answer 1

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:

`22`

We will first see how to deal with the percentage ( 0.2% ) and the starting number which is an unknown. So lets suppose:

`\text{Starting number = x}`

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:

`\begin{gathered} \text{Starting number }\cdot\text{ Percentage} \\ x\cdot(0.2)/(100) \end{gathered}`

Then we will equate the above expression to the resultant as follows:

`x\cdot(0.2)/(100)\text{ = 22}`

Now we have aa full fledged equation. We can easily manipulate and solve for the unknown number ( x ) as follows:

`\begin{gathered} x\cdot0.2\text{ = 2200} \\ x\text{ = }(2200)/(0.2) \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 11,000}} \end{gathered}`

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:

`\textcolor{#FF7968}{11,000}`