Q.2. You know that 17 = 0.142857. Can you predict what the decimal expansion of 27,37,47,57,67 are without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of 17 carefully.]

Solution:

Yes. We can be done this by simply multiplying the RHS by the numerator, i.e., 2, 3, 4 etc.

27=2×0.142857=0.285714

37=3×0.142857=0.428571

47=4×0.142857=0.571428

57=5×0.142857=0.714285

67=6×0.142857=0.857142