Question

Please help me with number 9

Answer 1

I’m happy to help!
For this problem, it is asking for a percentage error, which is basically how far off the student was from the true value. (But in percentages)
First, we need to find how far off the student was in millimeters, which is calculated by finding the difference between the guess and the true value:
13-12.5=0.5
So the student was 0.5 millimeters off of the total, from here, we can use this number to find our answer.
Percentages also have regular number counterparts. For example, 1 is 100%, because you have one whole thing. 0.5 is 50% because 0.5 is half of a whole number. .33 is 33% etc.
To calculate how far the guess was from the actual amount, we divide the difference (0.5) by the true value (12.5)
0.5/12.5=0.04
0.04 converted to a percentage is 4%. (You move the decimal two places to the left, or multiply by 100)
This works because you can calculate how much a value takes up of the total by dividing. For example, to find out how much 1 takes up of 4, you would calculate 1/4, which equals .25, or 25%, and we know this is true.
I hope this helps!

Answer 2

well, it was truly 12.5 mL, however she said 13 mL, well, she was off by 13 - 12.5 = 0.5 mL.

Now, if we take 12.5(origin amount) to be the 100%, what is 0.5 off of it in percentage?

`\begin{array}{ccll} Amount&\%\\ \cline{1-2} 12.5 & 100\\ 0.5& x \end{array} \implies \cfrac{12.5}{0.5}~~=~~\cfrac{100}{x} \implies 12.5x=50 \\\\\\ x=\cfrac{50}{12.5}\implies x=\stackrel{\%}{4}`