Question 4.2.20

A poem written by Madhava of Sangamagrama says, ‘$2,\!827,\!433,\!388,\!233$ is, as the wise say, the circumference of a circle whose diameter is $900,\!000,\!000,\!000$’. The ratio of a circle’s circumference to its diameter is a very important number which we’ll be studying later, called ‘pi’. Find pi to ten decimal places. Show answer

\begin{align*}\shortdiv{\ms{2}\ms{8}\ms{.}\ms{2}\ms{7}\ms{4}\ms{3}\ms{3}\ms{3}\ms{8}\ms{8}\ms{2}\ms{3}\ms{3}}{9}{\ms{}\ms{3}\ms{.}\ms{1}\ms{4}\ms{1}\ms{5}\ms{9}\ms{2}\ms{6}\ms{5}\ms{3}\ms{5}\ms{9}}{\ms{}\ms{}\ms{^1}\ms{^3}\ms{^1}\ms{^5}\ms{^8}\ms{^2}\ms{^5}\ms{^4}\ms{^3}\ms{^5}\ms{^8}}\end{align*} So pi to ten decimal places is $3.1415926536$.