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If you were only multplying 10 and 0.9, then you would get 9.
However, you are multiplying 10 by 0.9r, which is 0.99999999999999... nine's out to infinity.
0.999999999999999999999 * 10 = 9.9999999999999999999999999.
Trust me, having been through too many years of Algebra, Calculus, and other maths, there are about four different ways to prove that 0.9 repeating is EXACTLY equal to 1.
The geometric series mentioned above is one of them... the algebra is another. The simple fractional one is yet another. 1/3 = 0.3repeating, 2/3 = 0.6repeating, and 3/3 = (1/3 * 3)... which equals 0.9repeating, but as we all know, 3/3 = 1. Or, you could break it down into ninths.
1/9 = 0.11111...
2/9 = 0.22222....
3/9 = 1/3 = 0.3333333333...
Keep on going... 8/9 = 0.888888...
9/9 = 0.999999999, but a number divided by itself is 1. So they are the same.
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"The power of accurate observation is frequently called cynicism by those who don't have it." - George Bernard Shaw
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