What can the maximum number of digits be in the recurring block of digits in the decimal expansion of $$\frac{1}{17}$$? Perform the division to check your answer.

Asked by Vishal kumar | 1 year ago |  224

Solution :-

We need to find the number of digits in the recurring block of $$\frac{1}{17}$$.

Let us perform the long division to get the recurring block of $$\frac{1}{17}$$.

We need to divide 1 by 17, to get

We can observe that while dividing 1 by 17 we get 16 number of digits in the repeating block of decimal expansion which will continue to be 1 after carrying out 16 continuous divisions.

Therefore, we conclude that $$\frac{1}{17}$$ = 0.0588235294117647..... or $$\frac{1}{17}$$ = $$0.\overline{0588235294117647}$$, which is a non-terminating and recurring decimal.

Answered by Vishal kumar | 1 year ago

Related Questions

Visualise the representation of 5.37̅ on the number line upto 5 decimal places, that is upto 5.37777.

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.

Visualise 2.665 on the number line, using successive magnification.

Find whether the following statements are true or false:

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.

Represent $$\sqrt{10.5}$$  on the real number line.
Represent $$\sqrt{9.4}$$  on the real number line.