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.]

personReliable Education Group

April 20, 2022

Solution:

$https://latex.codecogs.com/svg.image?\inline \frac{1}{7}=0.\overline{142857}$

Hence $https://latex.codecogs.com/svg.image?\inline 2\times \frac{1}{7}=2\times 0.\overline{142857} = 0.\overline{285714}$

$https://latex.codecogs.com/svg.image?\inline 3\times \frac{1}{7}=3\times 0.\overline{142857} = 0.\overline{428571}$

$https://latex.codecogs.com/svg.image?\inline 4\times \frac{1}{7}=4\times 0.\overline{142857} = 0.\overline{571428}$

$https://latex.codecogs.com/svg.image?\inline 5\times \frac{1}{7}=5\times 0.\overline{142857} = 0.\overline{714285}$

$https://latex.codecogs.com/svg.image?\inline 6\times \frac{1}{7}=6\times 0.\overline{142857} = 0.\overline{857142}$

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