Question

Consider the following repeating decimal. 0.819 (a) Write the repeating decimal as a geometric series. 0.819 - (b) Write the
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Answer #1

0.8\overline{19}

(a) 0.8\overline{19} = 0.819191919...... = 0.8+0.019+0.00019+0.0000019+......

= 0.8+ 0.019 + 0.019x(0.01)+0.019x(0.01)2+........

0.819 = 0.8 +Σο.019(0.01) n=0

(b) Sum of geometric series with infinite number of terms and common ratio less than1 = a/(1-r)

Sum = 0.8+0.019/(1-0.01) = 4/5+19/990 = 811/990

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Consider the following repeating decimal. 0.819 (a) Write the repeating decimal as a geometric series. 0.819...
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