Q: if{-3/4, sqrt3, 3/sqrt3, sqrt(25/5), 20, 1.11222, 2.5015132,..., 626/262}, find the following 1) Rational numbers? 2) Irrational numbers?

Question
Irrational numbers
asked 2021-01-19
\(\displaystyle{Q}:{\quad\text{if}\quad}{\left\lbrace-\frac{{3}}{{4}},\sqrt{{3}},\frac{{3}}{\sqrt{{3}}},\sqrt{{\frac{{25}}{{5}}}},{20},{1.11222},{2.5015132},\ldots,\frac{{626}}{{262}}\right\rbrace}\),
find the following
1) Rational numbers?
2) Irrational numbers?

Answers (1)

2021-01-20
Rational number:
Rational numbers are the numbers that can be expressed in the form of a ratio \(\displaystyle{\left(\frac{{P}}{{Q}}{\quad\text{and}\quad}{Q}\ne{0}\right)}\)
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.
\(\displaystyle-\frac{{3}}{{4}}\) It is a rational number.
\(\displaystyle\sqrt{{9}}={3}\) It is a rational number.
\(\displaystyle\frac{{3}}{\sqrt{{3}}}=\sqrt{{3}}\) It can not be simplified more, so, it is a irrational number.
\(\displaystyle\sqrt{{\frac{{25}}{{5}}}}=\sqrt{{5}}\) It can not be simplified more, so, it is a irrational number.
\(\displaystyle{20}=\frac{{20}}{{1}}\) it is a rational number.
PSK1.11222 it is a rational number because 2 is repeating here.
PSK5.5015132 it is non-recurring and non-terminating. So, it is a irrational number.
\(\displaystyle\frac{{626}}{{262}}\) it is a rational number.
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