Question

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$\huge \tt \red{Question}$

You know that 1/7 = 0.142857. 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?
[Hint: Study the remainders while finding the value of 1/7 carefully.]​

Answer 1

Answer:

Given,

7

1

=0.

142857

.

Then,

7

2

=2×

7

1

=2×0.

142857

=0.

285714

7

3

=3×

7

1

=3×0.

142857

=0.

428571

7

4

=4×

7

1

=4×0.

142857

=0.

571428

7

5

=5×

7

1

=5×0.

142857

=0.

714285

7

6

=6×

7

1

=6×0.

142857

=0.

857142

Here, the first digit in the decimal expansion continued in the repeated numbers afterwards.