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Question Number 36103 by mondodotto@gmail.com last updated on 28/May/18

convert 0.26999999...into fraction (a/b) where a≠0

$$\boldsymbol{\mathrm{convert}}\:\mathrm{0}.\mathrm{26999999}...\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{fraction}}\: \\ $$$$\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}\:\boldsymbol{\mathrm{where}}\:\boldsymbol{\mathrm{a}}\neq\mathrm{0} \\ $$

Answered by MJS last updated on 28/May/18

=((26)/(100))+(9/(900))=((27)/(100))

$$=\frac{\mathrm{26}}{\mathrm{100}}+\frac{\mathrm{9}}{\mathrm{900}}=\frac{\mathrm{27}}{\mathrm{100}} \\ $$

Commented by mondodotto@gmail.com last updated on 28/May/18

but 27/100 ≠0.26999999... why

$$\mathrm{but}\:\mathrm{27}/\mathrm{100}\:\neq\mathrm{0}.\mathrm{26999999}... \\ $$$$\mathrm{why} \\ $$

Commented by MJS last updated on 29/May/18

3×(1/3)=3×.333.....=.999... but 3×(1/3)=1 ⇒ ⇒ .999...=1

$$\mathrm{3}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{3}×.\mathrm{333}.....=.\mathrm{999}...\:\mathrm{but}\:\mathrm{3}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{1}\:\Rightarrow \\ $$$$\Rightarrow\:.\mathrm{999}...=\mathrm{1} \\ $$

Answered by Rio Mike last updated on 28/May/18

round up 0.27⇒ ((27)/(100))

$$\mathrm{round}\:\mathrm{up}\: \\ $$$$\mathrm{0}.\mathrm{27}\Rightarrow\:\frac{\mathrm{27}}{\mathrm{100}} \\ $$

Answered by Penguin last updated on 28/May/18

x=0.26999... 100x=26.999... 1000x=269.999... 900x=243 x=((243)/(900)) x=((27)/(100))

$${x}=\mathrm{0}.\mathrm{26999}... \\ $$$$\mathrm{100}{x}=\mathrm{26}.\mathrm{999}... \\ $$$$\mathrm{1000}{x}=\mathrm{269}.\mathrm{999}... \\ $$$$\mathrm{900}{x}=\mathrm{243} \\ $$$${x}=\frac{\mathrm{243}}{\mathrm{900}} \\ $$$${x}=\frac{\mathrm{27}}{\mathrm{100}} \\ $$

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