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According to Modern Atomic Theory:

The ratio in which the different atoms combine may be fixed and integral but may not always be simple.

The example given is that in sugar molecule the ratio of $\ce{C,H}$ and $\ce{O}$ atoms is $12:22:11$ which is not simple.

Well, what I see here is that 12,22 and 11 are whole numbers, then why is this not a simple ratio?

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The ratio of C, H and O atoms of 12:22:11 is likely to be sucrose. Glucose has a simpler ratio of 1:2:1 (even though it has 6 carbons). The usual context for presenting the theory is with inorganic compounds with no more than a 2:3 or 3:5 ratio. With this limitation, they use the words simple ratio since the numbers are small and can easily be found. The ratio of 12:22:11 could be confused with another ratio if your calculations are off by 20%.

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It is often not true within inorganic chemistry (isomorphous substitution, fractional valences; e.g., ruby, sapphire). Discrete organics are overall exact single compositions. Polymers are not. Hydrocarbons have simple empirical formulas. Add heteroatoms and all bets are off.

Hemoglobin is $\ce{C2952H4664O832N812S8Fe4}$. Every high molecular weight Kraton thermoplastic elastomer triblock polymer contains a single atom of silicon at its exact middle. Plasma-drawn Spectra ultra-high molecular weight gel-crystallized polyethylene, some 20 times by weight stronger than steel cable, is $\ce{CH2}$.

Dicoronylene: $\ce{C48H20}$
Bacitracin: $\ce{C66H103N17O16S}$

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