Question

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1.28 what is a rational number equivalent to this

Answer 1

1.282828...
=1+0.28+0.0028+0.000028+...
=1+28(0.01+0.0001+0.000001+...)
\[=1+28\left( \frac{ 1 }{ 100 }+\frac{ 1 }{ 10000 }+\frac{ 1 }{ 1000000 }+...\right)\]
find r then\[s _{\infty}=\frac{ a }{ 1-r }\]
then simplify

Answer 2

or let x=1.282828...
100x=128.282828..
100x-x=128
99x=128
x=?

Answer 3

sorry correction
99x=127
x=?