Question

An approximate value of \[\pi \] is

Answer 1

Hint: The irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
\[\pi \] is an irrational number some use rational expression to estimate \[p\mathop i\limits^{} \] like \[\dfrac{{22}}{7}\] (This rational expression is only accurate to a couple of decimal places)

Complete step by step solution:
The approximate value of \[\pi \]is \[3.14159265\]or \[\dfrac{{22}}{7}\]
Two rational approximations to \[\pi \], namely.
\[\dfrac{{22}}{7} = 3.\overline {142857} \]
\[\dfrac{{355}}{{113}} = 3.1415929\] {=is for approximate value}
\[ \Rightarrow 3.141592 < \pi < 3.1415927\]

Hence correct answer is \[3.14\](option C)

Note: As we can see in the result, it has an infinite number of digits after the decimal point. Many square roots are also irrational since they cannot be reduced to fractions. Always remember When irrational numbers are encountered by a computer program, they must be estimated. If a number can be expressed as a ratio of two integers, it is rational.
The most accurate fraction equivalent to \[\pi \] is \[\dfrac{{355}}{{113}}\]