Question

Represent the number in rational form $0.\overline{47}$

• A. 47/100
• B. 47/99
• C. 47/999
• D. 47/10

Answer 1

The correct option is B 47/99

$0.\overline{47}=\mathrm{0.47474747...........}=0.47+0.0047+0.000047+......AninfiniteGpwithcommonratio=\left(\frac{1}{100}\right)\therefore 0.\overline{47}=0.47\cdot \left(\frac{1}{1-\left(\frac{1}{100}\right)}\right)=0.47\cdot \left(\frac{1}{\left(\frac{99}{100}\right)}\right)=\left(\frac{47}{99}\right)$