Question 5: What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer.
Thus, maximum number of digits in the repeating block is 17.
Question 6: Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy.
Answer: For having terminating decimal expansions, the denominator should have either 2 or 5 or both as factor. So, q must have either 2 or 5 or both.
`1/3` = 0.3 non-terminating repeating
`1/6` = 0.16 non-terminating repeating
`1/7` = 0.142857 non-terminating repeating
`1/9` = 0.1 non-terminating repeating
Question 7: Write three numbers whose decimal expansions are non-terminating non-recurring.
Answer: Non-terminating non-recurring numbers are known as irrational numbers. Irrational numbers cannot be expressed in the form of p/q where q≠0.
Following are the possible numbers:
Question 8: Find three different irrational numbers between the rational numbers 5/7 and 9/11.
Answer: 5/7 = 0.714285714285…….. and 9/11 = 0.8181818………
Possible irrational numbers between them can be as follows:
Note: Non-terminating non-recurring numbers are known as irrational numbers. Irrational numbers cannot be expressed in the form of p/q where q≠0. Numbers given above cannot be expressed in the form of p/q and hence are irrational.
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