Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = $\frac{ c}{d}$ . This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Question

cdquestions Admin · Accepted Answer

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  $\frac{ c}{d}$  fraction is irrational.  Hence, π is irrational.

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π =\(\frac{ c}{d}\). This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions