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State whether 1.456bar on 4 is rational |
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Answer» Let x=1.456456......... eq-110x=14.56456100x=145.64561000x=1456.456...............eq-2eq-2_eq-11000x-x=1456.456-1.456456999x=1455x=1455/999 {tex}\\begin{array}{l}\\mathrm{let}\\;\\mathrm x=1.\\overline{456}\\\\\\mathrm{then}\\;1000\\mathrm x=1456.\\overline{456}\\\\1000000=1456456.\\overline{456}\\\\\\mathrm{subtracting}\\;\\mathrm{we}\\;\\mathrm{get}\\\\999000\\mathrm x=1455000\\\\\\mathrm x=\\frac{1455000}{999000}=\\frac{1455}{999}=\\frac{485}{333}\\\\\\end{array}{/tex}Hence\xa0the number is in p/q ,so it is a rational |
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