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State whether 1.456bar on 4 is …

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State whether 1.456bar on 4 is rational

Posted by Swati Srivastava 6 years, 7 months ago

CBSE > Class 10 > Mathematics

2 answers

Anbu Mani 5 years, 1 month ago

Let x=1.456456......... eq-1 10x=14.56456 100x=145.6456 1000x=1456.456...............eq-2 eq-2_eq-1 1000x-x=1456.456-1.456456 999x=1455 x=1455/999

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Ram Kushwah 6 years, 7 months ago

{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 the number is in p/q ,so it is a rational

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