Sequences and Series — Maths STD 11 Science — Question
Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSequences and Series2 Marks
Question
Express the following recurring decimals as rational numbers.
$51.0 \overline{2}$
✓
Answer
$51.0 \overline{2}=51.0222 \ldots=51+0.02+0.002+0.0002+\ldots .$.The terms $0.02, 0.002, 0.0002,…$ are in G.P.
$\therefore a=0.02, r=\frac{0.002}{0.02}=0.1,|r|=|0.1|<1$
$\therefore$ Sum to infinity exists.
$\therefore$ Sum to infinity
$=51+\frac{a}{1-r}=51+\frac{0.02}{1-0.1}$
$=51+\frac{0.02}{0.9}$
$=51+\frac{2}{90}$
$=51+\frac{1}{45}$
$=\frac{2296}{45}$
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