Ananya observes that 1/7 = 0.142857..., 2/7 = 0.285714..., 3/7 = 0.428571..., all with a 6-digit repeating block. For a fraction k/7 (k not a multiple of 7), what is the length of the repeating block of its decimal expansion?

Question

Accepted Answer

6. All non-zero proper fractions with denominator 7 have the same period as 1/7, namely 6 (they are cyclic permutations of 142857). So the repeating block length is 6.

Ananya observes that $\frac{1}{7} = 0.142857..., \frac{2}{7} = 0.285714..., \frac{3}{7} = 0.428571...$ , all with a 6-digit repeating block.
For a fraction $\frac{k}{7} (k$ not a multiple of 7), what is the length of the repeating block of its decimal expansion?

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More Class 10 Decimal Expansions practice

Ananya observes that 71​=0.142857...,72​=0.285714...,73​=0.428571..., all with a 6-digit repeating block.For a fraction 7k​(k not a multiple of 7), what is the length of the repeating block of its decimal expansion?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Decimal Expansions practice

Ananya observes that $\frac{1}{7} = 0.142857..., \frac{2}{7} = 0.285714..., \frac{3}{7} = 0.428571...$ , all with a 6-digit repeating block.
For a fraction $\frac{k}{7} (k$ not a multiple of 7), what is the length of the repeating block of its decimal expansion?