Ramanujanโs formula for ฯ gives an accurate value of ฯ up to six decimal places, even using just the first term of an infinite series. This single term alone is sufficient to calculate the circumference of the Earth with a maximum error of only about one meter.
It is worth noting that while Ramanujanโs formula achieves this accuracy with just one term, the Leibniz series requires around five million terms to reach the same precision.
Each additional term in Ramanujanโs series adds roughly eight more correct decimal places to the value of ฯ. Although the formula is extraordinarily effective, there is still no complete understanding of how Ramanujan derived the specific constants in it, such as 9801 and 1103.