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23/05/2021 12:36 pm
Topic starter
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?
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23/05/2021 12:38 pm
\(\frac{1}{7}\) = \(\overline {0.142857}\)
∴ \(2 \times \frac{1}{7}\) = 2 x \(0.\overline{142857}\) = \(0.\overline{285714}\)
\(3 \times \frac{1}{7}\) = 3 x \(0.1\overline{42857}\) = \(0.4\overline{28571}\)
\(4 \times \frac{1}{7}\) = 4 x \(0.1\overline{42857}\) = \(0.\overline{571428}\)
\(5 \times \frac{1}{7}\) = 5 x \(0.1\overline{42857}\) = \(0.7\overline{14285}\)
\(6 \times \frac{1}{7}\) = 6 x \(0.\overline{142857}\) = \(0.8\overline{57142}\)
This post was modified 3 years ago by Raavi Tiwari