$5.63\div{0.01} = \frac{5.63}{0.01}$
$ = \frac{\frac{563}{100}}{\frac{1}{100}}=\frac{563}{100}\times\frac{100}{1}=563$
Statement - 1: Rational number can even be simply integers which can be further represented as $\frac{\text{p}}{\text{q}}$ form. So statement $1$ is false
Statement - 2: Any number divided by $0$ is not defined. So statement $2$ is true.
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 $100 - 99.999 = 100.000 - 99.999 = 0.001$
$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
$=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}$ $\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]$
$=\frac{5\times3+(-7)\times2+2\times4}{12} (LCM$ of $3, 4$ and $6 = 12)$
$=\frac{15-14+8}{12}$
$=\frac{9}{12}$
$=\frac{9\div3}{12\div3} ($Dividing numerator and denominator by $3)$
$=\frac{3}{4}$
Hence, the correct answer is option $(a).$
${125.625}\div{0.5} = \frac{125625}{1000}\times\frac{10}{5}$
$ = \frac{25125}{100} = {251.25}$
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 $(a).$
$\frac{2}{3} = {0.67}$ It is clear that $0.67$ lies between $0$ and $1$