Question

Write 0.05 as a fraction. A) 1 12 B) 1 15 Eliminate C) 1 18 D) 1 9

Answer 1

$x=0.0\overline{5}\\\\x=0.0555...\qquad\text{multiply both sides by 10}\\\\10x=0.555...\qquad\text{multiply both sides by 10}\\\\100x=5.555...\\\\\text{Make the difference:}\\\\100x-10x=5.555...-0.555...\\\\90x=5\qquad\text{divide both sides by 90}\\\\x=\dfrac{5}{90}\\\\x=\dfrac{5:5}{90:5}\\\\x=\dfrac{1}{18}\\\\Answer:\ \boxed{0.0\overline{5}=\dfrac{1}{18}}\to\boxed{C)}$