Ex 1.3 Class 9 Maths| NCERT Solutions for 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:
(i) We have, 36/100 = 0.36
Thus, the decimal expansion of 36/100 is terminating.
(ii) Dividing 1 by 11, we have
Thus, the decimal expansion of 1/11 is non-terminating repeating.
(iii)
Dividing 33 by 8, we get
∴ 33/8 = 4.125. Thus, the decimal expansion is terminating.
(iv) Dividing 3 by 13, we get
Here, the repeating block of digits is 230769
∴ 3/13 = 0.23076923…
Thus, the decimal expansion is non-terminating repeating.
(v) Dividing 2 by 11, we get
Here, the repeating block of digits is 18.
∴ 2/11 = 0.1818… = 0.18
Thus, the decimal expansion is non-terminating repeating.
(vi) Dividing 329 by 400, we get
∴ 329/400 = 0.8225. Thus, the decimal expansion is terminating.
Ex 1.3 Class 9 Maths | NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
Question 2.
Ex 1.3 Class 9 Maths | NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
Question 5.
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 117? Perform the division to check your answer.
Solution:
In 117, In the divisor is 17.
Since, the number of entries in the repeating block of digits is less than the divisor, then the maximum number of digits in the repeating block is 16.
Dividing 1 by 17, we have
Ex 1.3 Class 9 Maths| NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
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 that 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Solution:
Let us look decimal expansion of the following terminating rational numbers:
We observe that the prime factorisation of q (i.e. denominator) has only powers of 2 or powers of 5 or powers of both.
Ex 1.3 Class 9 Maths Question 7.
Write three numbers whose decimal expansions are non-terminating non-recurring.
Solution:
√2 = 1.414213562 ………..
√3 = 1.732050808 …….
√5 = 2.23606797 …….
Ex 1.3 Class 9 Maths Question 8.
Find three different irrational numbers between the rational numbers 57 and 911.
Solution:
We have,
(i) 0.750750075000 …..
(ii) 0.767076700767000 ……
(iii) 0.78080078008000 ……
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