Numbas has failed

a) The correct way to calculate the percentage is: $\dfrac{\text{recorded}}{\text{total possible}}\times100$.

This is because you want the amount that you recorded as a fraction of the total and then you multiply by 100 to get this as a percentage. 

b) Using the above formula the correct calculation is $\frac{\var{r}}{\var{t}}\times 100$, by substituting in the given values. 

c) Then the correct final value is $\var{precround(r/t*100,1)}$% using the above calculation. We could probably have guessed that this was the correct percentage as ${\var{r}}$ is less than $\var{t}$ so it cannot be greater than $100$% and $\var{r}$ is larger than half of ${\var{t}}$ so the only probable solution is that $\var{r}$ is $\var{precround(r/t*100,1)}$% of $\var{t}$.

You have to give out the drugs at a ratio $\var{a}:\var{b}$.

There are ($\var{a}+\var{b}$) = $\var{a+b}$ parts in total.

Divide the $\var{c} \text{g}$ by $\var{a + b}$ to get one part, and multiply by $\var{a}$ to get the amount of drug A to administer.

$(\var{c}\div\var{a+b})\times\var{a} = \var{precround((c/(a+b))*a,2)}$g of drug A is given (accurate to 2 decimal places)

Calculate separately the percentage of employees who are female and working on the project, and the percentage who are male and working on the project, and add them together.

1. Females

30% of the department is female and 20% of females are working on the project, hence the proportion of workers who are female and working on the project is 20% of 30% of the workers.

In terms of fractions this is \[ \frac{\var{femaleproject}}{100} \times \frac{\var{females}}{100} = \frac{\var{femaleproject*females}}{10000} = \frac{\var{depfemaleproject}}{100}\] of the workers, ie 6%.

So 6% of the departmental staff are working on the project and female.

2. Males

70% of the department is male and 10% of males are working on the project, hence the proportion of workers who are male and working on the project is 10% of 70% of the workers.

In terms of fractions this is \[ \frac{\var{maleproject}}{100} \times \frac{\var{males}}{100} = \frac{\var{maleproject*males}}{10000} = \frac{\var{depmaleproject}}{100}\] of the workers, ie 7%.

So 7% of the departmental staff are working on the project and male.

So the total percentage of departmental staff working on the project is $\var{depfemaleproject}\% + \var{depmaleproject}\% = \var{project}\%$.

a)

There are $10^6 \mu$m in 1m so when converting $\var{small}$$\mu$m to metres we divide by $10^6$:

$\var{small}$$\mu$m = $\var{small/(10^6)}$m.

There are 100cm in 1m, so when converting to cm divide by 100 : $\var{small/(10^6)}$m = $\var{small/(10^4)}$cm.

$\var{small}$$\mu$m = $\var{small/(10^4)}$cm.

b)

There are 1000ml in a litre, to convert $\var{liquid}$ml into litres we divide by 1000.

$\var{liquid}\div1000$ = $\var{liquid/1000}$ L.

c)

There are $10^6\mu$mol in one mole.

To convert $\mu$mol into moles you divide by $10^6$.

So $\var{mol}$$\mu$mol = $\var{mol/10^6}$ moles.

You need to convert everything into grams:
$\var{calories}$kg = $\var{calories*1000}$g
$\var{vitamins}$g = $\var{vitamins}$ g
$\var{prozac}$mg = $\var{prozac/1000}$g.

You have one bag protein powder = $\var{calories*1000}$g
You have 2 bags of vitamins = $\var{vitamins*2}$ g
You have 3 packets of Prozac = $\var{(prozac/1000)*3}$g
Adding together gives $\var{calories*1000}\text{g}+\var{vitamins*2}\text{g} + \var{(prozac/1000)*3}\text{g} $ = $\var{calories*1000+vitamins*2 + (prozac/1000)*3} $ g.