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Represent on the number line.
Draw a straight line on the number line and mark it is as OB = 9.3. Take BC of 1 unit. Find the mid-point D of OC and draw a semi-circle on OC while taking D as its centre.Now, draw a perpendicular to line OC passing through point B. Let it intersect the semi-circle at E. Taking B as centre and BE as radius, draw an arc intersecting number line at F. BF is
.
Classify the following numbers as rational or irrational: (i) (ii) (
) (iii)
(iv)
(v) 2π
(i) 
= 2 − 2.2360679…
= − 0.2360679…
Reason- The decimal expansion of this expression is non-terminating non-recurring. Hence, it is an irrational number.
(ii) 
Reason- It can be represented in the form of 
, It is a rational number.
(iii) 
Reason- It can be represented in the form of ,It is a rational number.
(iv) 
Reason- The decimal expansion of this expression is non-terminating non-recurring. Itt is an irrational number.
(v) 2π = 2(3.1415 …)
= 6.2830 …
Reason- The decimal expansion of this expression is non-terminating non-recurring. It is an irrational number.
Simplify each of the following expressions: (i) (ii)
(iii)
(iv)
(i) 
(ii) 
= 9 − 3 = 6
(iii) 
(iv) 
= 5 − 2 = 3
Recall, is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,
⋅ This seems to contradict the fact that
is irrational. How will you resolve this contradiction?#new_questionRepresent
on the number line.
There is no contradiction. When we measure a length with scale or any other instrument, we only obtain an approximate rational value. We never obtain an exact value. For this reason, we may not realise that either c or d is irrational. Therefore, the fraction 
is irrational. Hence, π is irrational.
Rationalise the denominators of the following: (i) (ii)
(iii)
(iv)
(i) 
(ii) 
(iii) 
(iv) 
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