2019 · Q28
What is 0.535353… + 0.533333… equal to, where in the first number the digits “53” repeat indefinitely and in the second number the digit “3” repeats indefinitely?
Elementary MathematicsNumber System
- A1.068686… (the digits “68” repeat)
- B1.066888… (the digit “8” repeats)
- C1.068068… (the digits “068” repeat)
- D1.068
Explanation
0.535353… = 1/2 + (35/99)/10 = 1/2 + 7/198, and 0.5333… = 1/2 + 1/30. Adding: 1 + 7/198 + 1/30 = 1 + 68/990 = 1.068686…, i.e. 1.0686 with '68' repeating.