Consider the following set of twelve numbers: 16 , ; 18 , ; 25 , ; 32 , ;3.1416,…

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

Consider the following set of twelve numbers:

\left\{\sqrt{16},\;\sqrt{18},\;\sqrt{25},\;\sqrt{32},\;3.1416,\;0.125,\;1.4142135\ldots,\;0.\overline{27},\;5.030303\ldots,\;\sqrt{81},\;\sqrt{2},\;2.5\right\}.

(i) Separate the numbers into two distinct sets—one containing all rational numbers and the other containing all irrational numbers. (ii) Express every number you have placed in the rational set either as an integer or in the form

\dfrac{p}{q}

, where

p,q\in\mathbb{Z}

and

q\neq0

. (iii) Choose any three numbers from your irrational set and, for each, state the two consecutive integers between which it lies on the number line.

Related theory

Real Number System
Rational and irrational numbers
Irrational numbers
Number Systems

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