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What ratio is commonly used as an alternative to 3.14?

User Izkeros
by
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2 Answers

3 votes

Answer:

it is typically 22 to 7

Explanation:

if you divide 22 by 7 you get 3.142857143...

User Razvans
by
8.5k points
4 votes

Answer:

22/7

Explanation:

You want to know a ratio commonly used as an alternative to 3.14 for an approximation to pi.

Approximations

The value 3.14 as an approximation of pi is obtained by simply truncating the value to 2 decimal places. That makes the approximation lower than the actual value by about 0.0507%.

Rational approximations can be found from the expression of pi as a continued fraction. Truncating that fraction at various points gives the approximations ...

22/7 . . . . high by about 0.0402%

333/106 . . . . low by about 0.0026%

355/113 . . . . . high by about 0.0000085%

22/7 is the most commonly used rational approximation of pi instead of 3.14.

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Additional comment

The continued fraction is non-repeating. It starts ...


3+\cfrac{1}{7+\cfrac{1}{15+\cfrac{1}{1+\cfrac{1}{292+\cfrac{1}{1+\dots}}}}}

User Oscar Barrett
by
8.1k points

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