It's just adding another 0 and 9 at the end

${\dfrac{100}{99}}$ = ${\dfrac{99+1}{99}}$ = ${1+\dfrac{1}{99}}$

Similarly, ${\dfrac{1000}{999}}$ = ${\dfrac{999+1}{999}}$ = ${1+\dfrac{1}{999}}$

Since, ${\dfrac{1}{99}}$ is greater than ${\dfrac{1}{999}}$

Therefore, ${\dfrac{100}{99}}$ > ${\dfrac{1000}{999}}$

Just take the reciprocal of the nos and compare since 0.99<0.999 therefore (100/99>1000/999)

Typical way I learnt:

$\displaystyle \frac{100}{99} : \displaystyle \frac{1000}{999} = 999 \times 100 : 99 \times 1000$ = 99900 : 99000. {Multiplied both sides by 999 $\times$ 99}

Therefore $\displaystyle \frac{100}{99} > \displaystyle \frac{1000}{999}$ as 99900 > 99000.

Answer: $\boxed{\displaystyle \frac{100}{99}}$

$\frac{100}{99}=\frac{100}{9}\left ( \frac{1}{11} \right )=\frac{100}{9}\left ( \frac{111}{1221} \right )$

$\frac{1000}{999}=\frac{100}{9}\left ( \frac{10}{111} \right )=\frac{100}{9}\left ( \frac{110}{1221} \right )$

So the greather is $\frac{100}{99}$

Just multiply-divide by 10

100/99=1.01010101 1000/999=1.001001001

Simply reciprocate the two get the decimal valus the smaller one is greater.

$\frac{100}{99} = \frac{1000}{990} > \frac{1000}{999}$

I just reciprocated both numbers. Knew that 999/1000 was larger than 99/100, so their reciprocals are in reverse order.

You could only say they were the same if it was 100/90 and 1000/900 because you can simplify by removing two zeroes at the end. You can't do that with other numbers like 999.