Using mass percentages

Percentage by mass is used commonly in chemistry and can be calculated as shown below.

%A =	m(A)	× 100%
	m(total)

This relationship shows that the decimal fraction of A is converted to a percentage by multiplying it by 100%.

In turn a percentage can be converted to the corresponding decimal fraction by dividing it by 100%.

Any of the two variables in the relationship above can be calculated if the other two are known.
The principles used in rearranging this equation to calculate m(total) are important and can be applied to any equation.

Using the percentage equation to calculate total mass where m(A) and %A are known

%A =

m(A)/m(total)

×100%

1. Divide both sides of the equation by 100%

2. Multiply both sides by m(total)

The result:

	%A	× m(total) = m(A)
	100%

3. Multiply both sides of the equation by 100%. Divide both sides of the equation by %A (the decimal equivalent of the percentage)

The result:

	m(total) =	m(A) ×100%
		%A

This is equivalent to converting the percentage to a decimal (step 1)
and dividing that decimal into the mass of A (steps 2 and 3).