[Hint: Study the remainders while finding the value of 1/7 carefully.]
NCERT Class 9 Maths chapter 1 NUMBER SYSTEMS
Page No. 14
Exercise 1.3
Question No. 2
You know that 1 7 = 0.142857142857142857…. Can you predict what the decimal expansions of 2/7,3/7,4/7,5/7,6/7 are, without actually doing the long division? If so, how?
Share
Without actual long division, the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are as follows:
2/7 = 2 × 1/7 = 2 × 0.142857142857142857… = 0.285714285714285714…
3/7 = 3 × 1/7 = 3 × 0.142857142857142857… = 0.428571428571428571…
4/7 = 4 × 1/7 = 4 × 0.142857142857142857… = 0.571428571428571428…
5/7 = 5 × 1/7 = 5 × 0.142857142857142857… = 0.714285714285714285…
6/7 = 6 × 1/7 = 6 × 0.142857142857142857… = 0.857142857142857142…