Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.1 - Real Numbers - 1.1 Exercises: 77

Answer

(a) $0.77777...=\frac{7}{9}$ (b) $0.28888...=\frac{13}{45}$ (c) $0.57575757...=\frac{19}{33}$

Work Step by Step

(a) $$x=0.77777...$$ $$10x=7.77777...$$ $$10x-x=7.77777..-0.77777...$$ $$9x=7.0$$ Hence $x=\frac{7}{9}$ (b) $$x=0.28888...$$ $$100x=28.88888...$$ $$10x=2.88888...$$ $$100x-10x=28.88888..-2.88888...$$ $$90x=26.0$$ Hence $x=\frac{26}{90}=\frac{13}{45}$ (c) $$x=0.57575757...$$ $$100x=57.57575757...$$ $$100x-x=57.57575757-0.57575757...$$ $$99x=57.0$$ Hence $x=\frac{57}{99}=\frac{19}{33}$
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