Expressing relative amounts

Suppose there is a chemical composition that contains 5 g of sugar and 45 g of water. One way of expressing the amount of sugar in relation to the whole would be to say the sugar content of the composition is 10%. And I am considering different ways of conveying the same idea.

Would it be correct to say:

(1) The amount of sugar relative to the whole composition of 1 is 0.1.

(2) The ratio by weight of sugar relative to the total amounts of sugar and water in the composition of 100 is 10.

The idea I want to convey with these sentences is that if the weight of the composition is first normalized or adjusted to 1, then the amount of sugar would work out to be 0.1. I know these are a bit clumsy but wonder if they need to be rewritten to be grammatical.

Solution 1:

The problem you are facing is not truly one of grammaticality. Rather, you are trying to state a ratio without making the formula incorrect. Both of your sentences, while clunky, are grammatical.

Translation is the art of making something understandable. As long as you are not changing the underlying scientific point, you can take a bit of license in the presentation.

To remove some of the clunkiness I would say:

When normalized to 1, the ratio of sugar in the solution is 0.1/1

or you could say

The ratio, by mass, of the solution is 5 grams of sugar to 45 grams of water. When normalized to 1, sugar is present in the ratio of 0.1/1.

or you could say

The composition of the solution is 10%; which means, that for every 1000 ml of water, we will have 10 grams of sugar.

Grammatically all of these sentences are correct. Mathematically, I believe they are correct, but check me on that.