Consider the following list of numbers: (-5, ;0, ; 7 2 , ;0.2020020002 , ; 16 , ; 5 )

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

Consider the following list of numbers: −5,  0,  72,  0.2020020002…,  16,  5-5,\;0,\;\frac{7}{2},\;0.2020020002\dots,\;\sqrt{16},\;\sqrt{5}. Answer the questions that follow. (i) For each number, state all the sets among N, W, Z, Q, R\mathbf{N},\,\mathbf{W},\,\mathbf{Z},\,\mathbf{Q},\,\mathbf{R} to which it belongs. (ii) Identify the number(s) that are irrational and justify your answer with suitable reasoning. (iii) Draw and label a Venn diagram of the sets N⊂W⊂Z⊂Q⊂R\mathbf{N}\subset\mathbf{W}\subset\mathbf{Z}\subset\mathbf{Q}\subset\mathbf{R}. Place any three numbers of your choice from the list in their appropriate regions.

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