You know that 17-0- 142857- Can you predict what the decimal expansions of 27-57-67- are- without actually doing the long division- if so- how-

17=0.142857 So, ⇒ 27=2(0.142857) =0.285714 ⇒ 37=3(0.142857) =0.428571 ⇒ 47=4(0.142857) =0.571428 ⇒ 57 ...

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Standard VII

Mathematics

Introduction: Decimal

You know that...

Question

You know that $\frac{1}{7} = 0. 142857$ . Can you predict what the decimal expansions of $\frac{2}{7}, \frac{5}{7}, \frac{6}{7},$ are, without actually doing the long division? if so, how?

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Solution

$\frac{1}{7} = 0.142857$

So,
$\Rightarrow$ $\frac{2}{7} = 2 (0.142857)$ $= 0.285714$

$\Rightarrow$ $\frac{3}{7} = 3 (0.142857)$ $= 0.428571$

$\Rightarrow$ $\frac{4}{7} = 4 (0.142857)$ $= 0.571428$

$\Rightarrow$ $\frac{5}{7} = 5 (0.142857)$ $= 0.714285$

$\Rightarrow$ $\frac{6}{7} = 6 (0.142857)$ $= 0.857142$

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

17=0.142857So,⇒27=2(0.142857)=0.285714⇒37=3(0.142857)=0.428571⇒47=4(0.142857)=0.571428⇒57=5(0.142857) =0.714285⇒67=6(0.142857) =0.857142

You know that $\frac{1}{7} = 0. 142857$ . Can you predict what the decimal expansions of $\frac{2}{7}, \frac{5}{7}, \frac{6}{7},$ are, without actually doing the long division? if so, how?