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Irina-Kira [14]
3 years ago
8

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

Mathematics
1 answer:
avanturin [10]3 years ago
7 0
22/7 = 3.142857...

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

-------

3 x 120 = 360

-------

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)

--------

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

22/7 = 3.142857...

355/113 = 3.14159292 (Calculator value)

π = 3.141592654

-------

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