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I'm wanting to apply 10-10-10 to my blackberries. 10-10-10 and 13-13-13 costs identical for the same quantity bags.

Since those numbers are just percentages, and in this case they are in equal ratios, can I safely apply the 13-13-13 instead of 10-10-10, and just apply 75% of the amount instead?

Why don't they just sell 33-34-33 (e.g. adding up to 100%), and people use very small quantities? Seems more economical than shipping useless filler.

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Yes, you can use it, in lesser quantities.

About the second question: the reason why we have not 33-34-33:

These number are the percent of weight of N,P, and K.

For example, N is a gas, so we need some molecules which includes N (it is impossible to have a solid 100, 0, 0 fertilizer) . Such molecules could include C, H, O, S, (and maybe other atoms). So they take some of the remaining weight to make 100%.

10-10-10 is probably not a dilute version of 13-13-13, but other molecules. If you are going professional, the molecules matter (and not just the numbers): some molecules decay very slowly (so it is cheap to do a heavy fertilization, but just every few years), some are very quick (so for emergency fertilization), some could acidify too much the soil (and they could have negative effect to other fertilizers), etc.

If you read carefully, the fertilizer should tell you which kind of molecules it contain. I confess that I never checked that the sum of all atoms in fertilizers (as advertised) will be really 100.

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    Having worked for a fertilizer company, the 10-10-10 is probably just a cut form of 13-13-13. The numbers will never add up to 100 as you mentioned because even if we had pure molecules there would still be some bonding agent (like the jelly that holds the antibiotics in your Neosporin). The fertilizer available to the masses are pretty always urea. Some smaller companies may use calcium nitrate because it is a byproduct of a particular reaction to extract Phosphorus, but it is rarely economical to do so and thus isn't done on large scales.
    – corsiKa
    Mar 19, 2018 at 17:26
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    Urea is used in fertilizer because it's a cheap form of NItrogen. Ammonium Sulfate and in the past Ammonium Nitrate was used because it is an Ammonium form of Nitrogen that is easier for plants to absorb, but it's more expensive than Urea. Urea generally requires soil bacteria to break it down or "oxidize" it into Ammonium or a form of nitrogen easily absorbed by plants. I grow cactus and dry soil does not sustain bacteria in sufficient numbers to process Urea, so I use Ammonium Sulfate. I mix it with the other two components (Potassium and Phosphorous) and have had excellent results.
    – Tim Nevins
    Mar 19, 2018 at 17:45

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