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Question Number 57222 by Tawa1 last updated on 31/Mar/19

$$\mathrm{Express}5.27\mathrm{in}\mathrm{form}\mathrm{of}\mathrm{a}\mathrm{series}\mathrm{and}\mathrm{show}\mathrm{that}\mathrm{is}\mathrm{equal}$$$$\mathrm{to}5\frac{5}{18}$$

Answered by Joel578 last updated on 01/Apr/19

$$5.2\stackrel{\mathrm{\_}}{7}=5.2+\frac{7}{{10}^2}+\frac{7}{{10}^3}+\frac{7}{{10}^4}+\frac{7}{{10}^5}+...$$$$=\frac{52}{10}+\frac{\frac{7}{{10}^2}}{1-\frac{1}{10}}$$$$=\frac{52}{10}+\frac{7}{90}$$$$=\frac{95}{18}=5\frac{5}{18}$$

Commented by Tawa1 last updated on 01/Apr/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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