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

Concept: Without doing long calculations we need to solve the fractions. For that we are given 1 number and its decimal value so using that we can solve others without long calculation.17 =0.14285727 =2×17 =2×0.142857 =0.28571437 =3×17 =3×0.142857 =0.42857147 =4×17 =4×0.142857 =0.57142857 =5×17=5×0.142857 =0.71428567 =6×17 =6×0.142857 =0.857142Hence, the correct option is 1.

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

Concept: Without doing long calculations we need to solve the fractions. For that we are given 1 number and its decimal value so using that we can solve others without long calculation.17 =0.14285727 =2×17 =2×0.142857 =0.28571437 =3×17 =3×0.142857 =0.42857147 =4×17 =4×0.142857 =0.57142857 =5×17=5×0.142857 =0.71428567 =6×17 =6×0.142857 =0.857142Hence, the correct option is 1.

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You know that $\frac{1}{7}$ =0.142857. Can you predict what the decimal expansions of $\frac{2}{7}$ , $\frac{3}{7}$ , $\frac{4}{7}$ , $\frac{5}{7}$ , $\frac{6}{7}$ are, without actually doing the long division? If so, how?

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0.285714, 0.428571, 0.571428, 0.714285, 0.857142

0.571428, 0.428571, 0.857142, 0.714285, 0.285714

0.857142, 0.714285, 0.571428, 0.428571, 0.285714

0.714285, 0.571428, 0.428571, 0.285714, 0.857142

answer is A.

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Detailed Solution

Concept: Without doing long calculations we need to solve the fractions. For that we are given 1 number and its decimal value so using that we can solve others without long calculation.