Class 9 Maths Chapter 1 Exercise-1.3 Solutions
Class 9 Maths Chapter 1 Exercise-1.3 Solutions is based on the decimal expansion of rational numbers as well as irrational numbers. You learn in this exercise that the decimal expansion of a rational number is either terminating or non-terminating recurring and the decimal expansion of an irrational number is always non-terminating and non-recurring. Also, you will find some questions where you have to convert a non-terminating recurring decimal expansion into p/q form. In addition to this, there are also questions where you need to write irrational numbers between a given pair of rational numbers.
1. Write the following in decimal form and say what kind of decimal expansion each has:
2. You know that 1/7 = 0.142857…. Can you predict what the decimal expansion of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how? [Hint: Study the remainders while finding the value of 1/7 carefully.]
3. Express the following in the form of p/q, where p and q are integers and q≠0.
4. Express 0.9999…. in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
5. What can the maximum number of digits in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.
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?
7. Write three numbers whose decimal expansions are non-terminating non-recurring.
8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.
9. Classify the following numbers as rational or irrational:
