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