Gujarat Board Textbook Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.3
Gujarat Board Textbook Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.3
GSEB Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.3
Question 1.
Write the following in decimal form and say what kind of decimal expansion each has
Solution:
The decimal expansion is non-terminating repeating.
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.
Solution:
Long division method
We observe that by long division method maximum number of digits in repeating block in the decimal expansion of 1/17 is 16, thus answer is verified.
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?
Solution:
We observe that the denominator of all the above rational numbers are of the form 2m x 5n i.e., the prime factorization of denominators has only powers of 2 or powers of 5 or both.
Question 7.
Write three numbers whose decimal expansions are non-terminating non-recurring.
Solution:
(i) 0.012012001200012…
(ii) 0.21021002100021000021…
(iii) 0.32032003200032000032…
Question 9.
Classify the following numbers as rational or irrational.
(iii) 0.3796
The decimal expression is terminating.
Hence 0.3796 is a rational number.
(iv) 7.478478…
∴ 7.478478… = 7.748
The decimal expansion is non-terminating recurring.
∴ 7.478478… is a rational number.
(v) 1.101001000100001…
∵ The decimal expansion is non – terminating non-recurring.
∴ 1.101001000100001… is an irrational number.
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