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Find the fifth digit

Source: 1971 AHSME Problem 13

April 19, 2014
algebrabinomial theoremAMC

Problem Statement

If (1.0025)10(1.0025)^{10} is evaluated correct to 55 decimal places, then the digit in the fifth decimal place is
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>5<spanclass=′latex−bold′>(E)</span>8<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>5\qquad <span class='latex-bold'>(E) </span>8
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