NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5
Ex 1.5 Class 9 Maths Question 1.
Classify the following numbers as rational or irrational:
(1) 2-
(2) (3+
)-
(3)
(4)
(5) 2π
Solution:(1) Irrational ∵ 2 is a rational number and is an irrational number.
∴ 2 – is an irrational number.
(∵ The difference of a rational number and an irrational number is irrational)
Classify the following numbers as rational or irrational:
(1) 2-
(2) (3+
)-(3)
(4)
(5) 2π
Solution:(1) Irrational ∵ 2 is a rational number and
is an irrational number.∴ 2 –
is an irrational number.(∵ The difference of a rational number and an irrational number is irrational)
(2) 3 + – = 3 (rational)
– = 3 (rational)
(3) =
(rational)
= (rational)
(4) 
(irrational) ∵ 1 ≠ 0 is a rational number and 
2 ≠ 0 is an irrational a/2 number.
∴ = is an irrational number.
(∵ The quotient of a non-zero rational number with an irrational number is irrational).
(5) 2π (irrational) ∵ 2 is a rational number and π is an irrational number.
∴ 2π is an irrational number, (∵ The product of a non-zero rational number with an irrational number is an irrational).
(irrational) ∵ 1 ≠ 0 is a rational number and 2 ≠ 0 is an irrational a/2 number.∴
= is an irrational number.(∵ The quotient of a non-zero rational number with an irrational number is irrational).
(5) 2π (irrational) ∵ 2 is a rational number and π is an irrational number.
∴ 2π is an irrational number, (∵ The product of a non-zero rational number with an irrational number is an irrational).
Ex 1.5 Class 9 Maths Question 2.
Simplify each of the following expressions :(1) (3 +
) (2 + a/2)
(2) (3 + ) (3- )
(3) ( + )2
(4) ( – ) ( + )
Solution:
Simplify each of the following expressions :(1) (3 +
) (2 + a/2)(2) (3 +
) (3- )(3) (
+ )2(4) (
– ) ( + )Solution:
Ex 1.5 Class 9 Maths Question 3.
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is
π =
. This seems to contradict the fact that it is irrational. How will you resolve this contradiction?
Solution:
Actually = 
which is an approximate value of π.
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is
π =
. This seems to contradict the fact that it is irrational. How will you resolve this contradiction?Solution:
Actually
= which is an approximate value of π.
Ex 1.5 Class 9 Maths Question 4.
Represent
on the number line.
Solution:
Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B, mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with center O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D
Then BD =. To represent on the number line. Let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with center B and radius BD, which intersects the number line at point E. Then, the point E represent .
Represent
on the number line.Solution:
Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B, mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with center O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D
Then BD =
. To represent on the number line. Let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with center B and radius BD, which intersects the number line at point E. Then, the point E represent .
Ex 1.5 Class 9 Maths Question 5.
Rationalise the denominators of the following:
(i)
(ii)
(iii)
(iv)
Solution:
Rationalise the denominators of the following:
(i)
(ii)
(iii)
(iv)
Solution:
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