 postillan4

2021-01-19

$Q:\phantom{\rule{1em}{0ex}}\text{if}\phantom{\rule{1em}{0ex}}\left\{-\frac{3}{4},\sqrt{3},\frac{3}{\sqrt{3}},\sqrt{\frac{25}{5}},20,1.11222,2.5015132,\dots ,\frac{626}{262}\right\}$,
find the following
1) Rational numbers?
2) Irrational numbers? Nathaniel Kramer

Rational number:
Rational numbers are the numbers that can be expressed in the form of a ratio $\left(\frac{P}{Q}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}Q\ne 0\right)$
and also if decimal number represents the number after the decimal is repeating, then it is a rational number.
Irrational numbers:
It is impossible to express irrational numbers as fractions or in a ratio of two integers, irrational numbers have endless non-repeating digits after the decimal point.
$-\frac{3}{4}$ It is a rational number.
$\sqrt{9}=3$ It is a rational number.
$\frac{3}{\sqrt{3}}=\sqrt{3}$ It can not be simplified more, so, it is a irrational number.
$\sqrt{\frac{25}{5}}=\sqrt{5}$ It can not be simplified more, so, it is a irrational number.
$20=\frac{20}{1}$ it is a rational number.
$1.11222$ it is a rational number because 2 is repeating here.
$5.5015132$ it is non-recurring and non-terminating. So, it is a irrational number.
$\frac{626}{262}$ it is a rational number.

Do you have a similar question?