Yes.
1/1,000 = 0.001
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10
No, taking ½ of a number is the same as dividing it by 2. Dividing a number by ½ is the same as multiplying it by 2.
1000
That is the definition of reciprocal.
If you have 1000 100s of something, that is the same as multiplying 1000 by 100, which is 100,000.