Question

What are the $1^{st}$ 100 digits of pi?

Answer 1

Hint: Since pi is also represented as$\pi $. As $\pi $is the symbol of representation of a particular ratio. Ratio of the circumference of a circle to its diameter is called $\pi$, which is always constant irrespective of the size of the circle. So we will go through the ways of computing the value of $\pi'$.

Complete step by step solution:
Moving ahead with the question, as asked to find out the 1st 100 value of $\pi $ . Since earlier there are only experimental ways through which we can find out the value of $\pi $ . And it came out that $\pi $ is a recurring non-repeating irrational number. So since very early there is always a race to find the most accurate value of $\pi $ .
Earlier people used to find out the value of $\pi $ through making the circle and finding the value of $\pi $ by taking the ratio of circumference of the circle to its diameter. And by several experiments they decided to round off the value of $\pi $ to the nearest decimal to solve some circular related problems with an accurate answer, which turned out to be 3.14.
Till now many other methods were discovered to find the value of $\pi $ , some mathematicians discovered the infinite series which relates the value of $\pi $ so closely. Some of them are;
\[\pi =\left( \dfrac{4}{1} \right)-\left( \dfrac{4}{3} \right)+\left( \dfrac{4}{5} \right)-\left( \dfrac{4}{7} \right)+\left( \dfrac{4}{9} \right).......\]
Take 4 and subtract 4 divided by 3. Then add 4 divided by 5. Then subtract 4 divided by 7. Continue alternating between adding and subtracting fractions with a numerator of 4 and a denominator of each subsequent odd number.
Other infinite series is;
\[\pi =3+\left( \dfrac{4}{2\times 3\times 4} \right)-\left( \dfrac{4}{4\times 5\times 6} \right)+\left( \dfrac{4}{6\times 7\times 8} \right)-.........\]
For this series, take three and start alternating between adding and subtracting fractions with numerators of 4 and denominators that are the product of three consecutive integers which increase with every new iteration. Each subsequent fraction begins its set of integers with the highest one used in the previous fraction.
These methods are now performed using different technologies to find the value of pi. And now people have found the value of all about trillion digits after decimal. Out of which value of pi with 1st 100 digits of pi is;
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067.

Note: Still people are finding the value of pi more accurately, using the different technologies we had developed till now, and success and finding its value for all about 30 trillion digits after the decimal.