Question

how do I find a whole number x so that the ratio x:113 is a better estimate for pi than 22/7 and 3.14

Answer 1

22/7 = 3.142857...

Let's see if we can beat this using a fraction with 113 as its denominator.

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3 x 120 = 360

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So, let's try out x = 360:

360/113 = 3.185.... (Too high)

How about x=350:

350/113 = 3.097... (Too low)

Let's try out x = 355:

355/113 = 3.14159292 (Calculator value)

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Let's now compare 22/7 and 355/113 to pi:

22/7 = 3.142857...

355/113 = 3.14159292 (Calculator value)

π = 3.141592654

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As we can see, 355/113 provides us with a better approximation of π. This means that x=355.