[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?

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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…