The value of 1.7̅ + 0.28̅9̅ − 1.39̅ is equal to:
2019
The value of 1.7̅ + 0.28̅9̅ − 1.39̅ is equal to:
- A.
0.58̅7̅
- B.
0.53̅6̅
- C.
0.66̅7̅
- D.
0.6̅6̅7̅
Attempted by 36 students.
Show answer & explanation
Correct answer: C
Convert the recurring decimals into fractions. 1.7̅ = 16/9. Also, 0.28̅9̅ = 0.2 + 0.08̅9̅ = 1/5 + 89/990 = 287/990, and 1.39̅ = 1.4 = 7/5. Now, 16/9 + 287/990 − 7/5 = 1760/990 + 287/990 − 1386/990 = 661/990 = 0.6676767.... So the repeating block is 67 after the first decimal digit, i.e., 0.66̅7̅. Hence, Option C is correct.