How to get an accurate result in the following problem? I just wanted to know simple how many percent 1.7 is smaller than 1.9 (and vice versa). What I did is: $\frac{1.7\cdot100}{1.9}= 89.4736842105$.. It means that 1.7 is smaller than 1.9 in 10.5263157895%. Later, to check it I calculate in the calculator: 1.7+10.5263157895% and I got: 1.87894736842. Why is it not the same? and what is the best shortest way to write the percent that I mentioned above (10.5263157895%)? 
 A: As someone who does markup and margin for fun, heres a quick explanation:
margin: the percentage as taken from a whole thing ( in this case 1.9).
markup: the percentage of a whole thing you add to it's value (in this case 1.7)
The reason the two don't equate is that the true value of the difference, is a different percentage of the different things 0.2 is $\frac{2}{17}$ of 1.7, and $\frac{2}{19}$ of 1.9 to convert between markup and margin we have a formula:$$\text{markup}=\frac{1}{1-\text{margin}}-1$$ plugging the numbers in will show, $$\frac{2}{17}=\frac{1}{1-\frac{2}{19}}-1$$ What you did was, in effect: $$\text{markup}=\text{margin}$$  Which if this was money, would potentially get you fired if you have a job. Or fool you into thinking, a sale will allow you to buy more/less than what it will. Or make you unable to buy certain quantities of your merchandise, or pay your employees if running a business. 
Here are some Applications by example:


*

*$$F=ma$$ Then by fixing the force F, we show that since m decreasing m by 20% decreases the product 20%, it increases the acceleration required/that happens, by $$25\%=\frac{1}{1-20\%}-1$$ 

*Suppose a government imposes a  consistent 10% income tax on all income via markup and margin, we can show that to make the same amount after taxes, as you did with no taxes, you now have to earn:$$\frac{1}{9}=\frac{1}{1-\frac{1}{10}}-1$$ more income to offset the tax.

*Suppose your area of the world, has 15% of doctors retiring, via markup and margin, we can show that each doctor remaining has to see: $$\frac{3}{17}=\frac{1}{1-\frac{3}{20}}-1$$ more patients to keep the number of patients being seen the same.

*Suppose you're going somewhere some distance d away. By markup and margin, going 40% faster than the speed limits the whole way there gets you there in :$$\frac{2}{5}=\frac{1}{1-\frac{2}{7}}-1$$ Less time, where margin was solved for (the important part in this example) via:$$\text{margin}=1-\frac{1}{1+\text{markup}}$$ Which is just our normal equation rearranged. under 29% saved time wise BTW. 
I could literally go on all day.
A: What you calculated is what percentage of $1.9$ should be subtracted from $1.9$ to get $1.7$. However, in the calculator you are doing $1.7$ plus the same percentage times $1.7$. The correct way to check would be $1.7 + \frac{10.5263157895}{100}\cdot 1.9$.
A: If you compare 1.7 to 1.9, you determine that 1.7 is smaller than 1.9 by 10.5263% of 1.9. It doesn't make sense to say it is smaller by some percent alone. 
But when you add that percent back, you are adding 10.5263% of 1.7, not of 1.9 -- so of course you won't get the same result.
What is true is that $1.7 + 10.5263\%\times 1.9 = 1.9$.
