Re: Which of the two values 10^(-2) and 10^(-3), is x more close

can anybody help with the above solution please.

number line = \frac{1}{10000}---- \frac{1}{1000} -- | --\frac{1}{100} ----\frac{1}{10}


(1) x is more closer to \frac{1}{10000} than to \frac{1}{10}

for this to be true shouldn't x have to be to the left of the center marked as | above and if x is the left of the center ,then shouldn't x be closer to \frac{1}{1000}than to \frac{1}{100}

I fail to see how x can be anywhere between \frac{1}{1000} and \frac{1}{100}and still be closer to \frac{1}{10000} than to \frac{1}{10}

lets say x is between \frac{1}{1000} and \frac{1}{100} but just slightly to the left of \frac{1}{100}, say x = \frac{1}{101}
now here x lies as shown \frac{1}{1000} -- | -- \frac{1}{101} --\frac{1}{100} so here it looks x is between 10^{-3} and 10 ^{-2} but closer to \frac{1}{10}, so this doesn't satisfy statement 1

lets say x =\frac{1}{999}here the position of x = \frac{1}{10000}---- \frac{1}{1000} --\frac{1}{999} --- | --\frac{1}{100} ----\frac{1}{10}

so here statement 1 holds and x is closer to \frac{1}{10000} .

So it seems to me for statement 1 to hold x has to be to the left of the center , marked as |in the number line, and in that case x will be closer to \frac{1}{1000} than to \frac{1}{100}, anywhere to the right of | and x becomes closer to \frac{1}{10} violating statement1 , so x has to be to the left of | for statement 1 to be true. so I am getting A as sufficient . Can anybody assist please?

thanks