$5.63\div{0.01} = \frac{5.63}{0.01}$
$ = \frac{\frac{563}{100}}{\frac{1}{100}}=\frac{563}{100}\times\frac{100}{1}=563$
values of rational numbers $x$ and $y$ is not given For any two rational numbers all three properties are correct as $x < y$ or $x
= y$ or $x > y$
There exists infinite number of rational numbers between any two rational numbers. i.e. in this case between $\frac{2}{5}$ and $\frac{4}{5}$.
We know that the reciprocal of the rational number $\frac{\text{a}}{\text{b}}\text{ is }\Big(\frac{\text{a}}{\text{b}}\Big)^{-1}=\frac{\text{b}}{\text{a}}$
$\therefore$ Reciprocal of $\frac{-3}{4}$
$=\Big(\frac{-3}{4}\Big)^{-1}$
$=\frac{4}{-3}$
$=\frac{4\times(-1)}{-3\times(-1)}$
$=\frac{-4}{3}$
Hence, the correct answer is option $(c).$
$\frac{-18}{5} = -3.6 - 4 < -3.6 < -3 - 3.6$ lies between $-3$ and $-4.$
Difference of $99.999$ and $100$ is $100 - 99.999 = 100.000 - 99.999 = 0.001$
The denominator of the rational number $-\frac{102}{119}$ is positivr.
In order to write the rational number in standerd form, divide its numerator and denominator by the $HCF$ of $102$ and $119.$
$HCF$ of $102$ and $119 = 17$
Dividing the numerator and denominator of $-\frac{102}{119}$ by $17,$
We have:
$-\frac{102}{119}=-\frac{102\div17}{119\div17}=-\frac{6}{7}$
Thus the standard form of $-\frac{102}{119}\text{ is }-\frac{6}{7}$
Hence, the correct answer is option $(a).$