Classes›Class 9›Maths›NCERT›The World of Numbers›Exercise 3.5›Q 5
QUESTION 5 Easy

We have seen that the repeating block of \(\frac{1}{7}\) is a cyclic number. Try to find more numbers (n) whose reciprocals \((\frac{1}{n})\) produce decimals with repeating blocks that are cyclic.

SOLUTION

\(17, 19, 23, 29,43...\) are some numbers whose reciprocals (\(\frac{1}{17}, \frac{1}{19}, \frac{1}{23}, \frac{1}{29}, \frac{1}{43},...\)) produce decimals with repeating blocks that are cyclic.
Example:
\(\frac{1}{17} = 0.\overline{0588235294117647}\)
\(\frac{1}{19} = 0.\overline{0526315789473684211}\)
\(\frac{1}{23} = 0.\overline{0434782608695652173913}\)