Offprint · Wondering About Pi · No. 3.1415

355/113

Six digits, six places.

About fifteen hundred years ago, the astronomer Zu Chongzhi gave two fractions for π. He called 22/7 the approximate ratio. He called 355/113 the close one.

Divide it out and it matches π to six decimal places, off by less than three ten-millionths.

No fraction with a smaller denominator comes closer. The next one that does is 52163/16604, which no one keeps anywhere.

closer3/122/7333/106355/113

Best fraction with a denominator up to 120: 355/113, off by 0.00000027. It stays the best until 16,604.

Figure Every denominator, and how close its best fraction gets. Higher is closer. A few stand far above their neighbors.

“355/113.” Wondering About Pi, no. 3.1415 (24 September 2026). wap.mom/355-113/