How to explain rational numbers, irrational numbers, and how they are different?

Question
Decimals
asked 2020-11-08
How to explain rational numbers, irrational numbers, and how they are different?

Answers (1)

2020-11-09
Step 1 To explain: a) Rational number. b) Irrational number. c) Difference between rational number and irrational number. Step 2 a) Rational number: A Rational number is a number that can be expressed in the form of a ratio p/q, where p and q are integers and \(\displaystyle{q}\ne{q}{0}\). Rational numbers are finite and has terminating or repeating decimals. Examples of rational numbers: \(\displaystyle{\frac{{{1}}}{{{2}}}},{\frac{{{7}}}{{{4}}}},\sqrt{{{81}}},{\frac{{{1}}}{{{100}}}}\) etc. \(\displaystyle{\frac{{{3}}}{{{4}}}}\) can be represented as 0.75 which is a terminating decimal. \(\displaystyle{\frac{{{2}}}{{{3}}}}\) can be represented as 0.6666 .... which is a repeating decimal. Step 3 b) Irrational number: An irrational numbers is a number that is not rational. Irrational numbers cannot be expressed as a fraction with integer values in the numerator and denominator. Irrational numbers are infinite and has non - terminating and non-repeating terms. When an irrational number is expressed in decimal form, it goes on forever without repeating. But both the numbers are real numbers and can be represented in a number line. Examples of irrational numbers: \(\displaystyle{\frac{{\sqrt{{{3}}}}}{{{2}}}},\pi,{0.131331333}\ldots.,{5}+\sqrt{{{3}}}\) Step 4 c) Difference between rational number and irrational number: PSK\begin{array}{|c|c|} \hline Rational\ number & Irrational\ number \\ \hline It\ is\ expressed\ in\ the\ ratio,\ where\ both\ numerator\ and\ denominator\ are\ the\ whole\ numbers & It\ is\ impossible\ to\ express\ irrational\ numbers\ as\ fractions\ or\ in\ a\ ratio\ of\ two\ integers \\ \hline It\ includes\ perfect\ squares & It\ includes\ surds\ ( we\ can't\ simplify\ a\ number\ to\ remove\ a\ square\ root ) \\ \hline The\ decimal\ expansion\ for\ rational\ number\ executes\ finite\ or\ recurring\ decimals & Here,\ non-terminating\ and\ non-recurring\ decimals\ are\ executed \\ \hline \end{array}ZSK
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