Question

What is the approximate value of \[\pi\]?

Answer 1

Hint: In order to find the approximate value of \[\pi\], we must consider the known value of \[\pi\] i.e. the rational value of \[\pi\]. Since we know that \[\pi\] is an irrational number, we cannot find the exact value of \[\pi\]. Instead we will be finding the approximate or the nearer value of \[\pi\].

Complete step by step answer:
Let us briefly discuss irrational numbers. Irrational numbers are those numbers that are real but cannot be expressed in the form of a fraction which means it cannot be expressed in the form of \[\dfrac{p}{q}\] where \[p,q\] are integers and \[q\ne 0\]. The decimal expansion of an irrational number is neither terminating nor recurring. We can find whether a number is irrational or not by trying to express the number in the \[\dfrac{p}{q}\] form. Irrational numbers are a part of real numbers which means that they obey all the properties of real numbers. The most common or known irrational numbers are \[\pi\], Euler’s number and Golden ratio.
Now let us find the approximate value of \[\pi\].
The rational form of \[\pi\] is \[\dfrac{22}{7}\]. This is considered as the approximate value of \[\pi\].
The decimal expansion of \[\dfrac{22}{7}\] would be \[\dfrac{22}{7}=3.1415...\]
\[\therefore \] The approximate value of \[\pi\] is \[\dfrac{22}{7}\].

Note: We can consider the value of \[\pi\] according to our convenience either the fractional form of the decimal form. We must have a note that the least common multiple of two irrational numbers may or may not exist. It obeys properties such as the addition and the multiplication.