# 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.

• People would be more likely to say 'ten to one' than 'a hundred to ten' Oct 10, 2019 at 16:41
• But it’s not 10% there are 5 parts sugar to 61 parts solution. Normalizing to 100 parts gives 8.2 parts per hundred. (8.2%)
– Jim
Oct 10, 2019 at 17:11
• Would you also consider using concentration? There are several ways to solve this at this site: m.wikihow.com/Calculate-the-Concentration-of-a-Solution. Oct 10, 2019 at 20:13
• They're not ungrammatical. But, they're all too clunky for scientific use. You'd just say 10%. And, if trying to be instructive you'd say 10% (5g sugar to 56g of water). But as @Jim points out, the math is wrong ... 56g of water is 56 ml of water. 10% solution would be 100 mg/ml. 5000mg/50ml ... A 1% solution is 1g/L. Oct 10, 2019 at 20:21
• Oct 10, 2019 at 22:02

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.

Your sentences are grammatically correct. However, they aren't just awkward; they border on unintelligible. It's also not clear to me why you are looking for an alternative to percent to express the mass of some mixture component relative to the mass of the mixture.

However, you could use any of:

...10% sugar by weight (in water)

...10% sugar in water (by mass)

...9:1 water:sugar ratio (by weight/mass)

...1 part sugar to 9 parts water (by weight/mass)

...1 mass unit sugar to 9 mass units water