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?
[Hint: Study the remainders while finding the value of \( \frac{1}{7}\) carefully.]
\( \frac{1}{7}=0.\overline{142857}\) or \( \frac{1}{7}\)= 0.142857.....
find the values of \( \frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7}\) and \( \frac{6}{7}\), without performing long divison.
\( \frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7}\) and \( \frac{6}{7}\) can be rewritten as \( 2\times \frac{1}{7},3\times \frac{1}{7},4\times \frac{1}{7}\), \( 5\times\frac{1}{7}\), and \( 6\times\frac{1}{7}\).
On substituting value of \( \frac{1}{7}\) = 0.142857..... , we get
Therefore, we conclude that, the values of \( \frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7}\) and \( \frac{6}{7}\), without performing long division. we get
Visualise the representation of \( 5.3\overline{7}\) on the number line upto 5 decimal places, that is upto 5.37777.
Visualise 2.665 on the number line, using successive magnification.
Find whether the following statements are true or false:
(i) Every real number is either rational or irrational.
(ii) π is an irrational number.
(iii) Irrational numbers cannot be represented by points on the number line.