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No fraction is truly the closest to the "actual value" of pi. Pi is a nonstop number, thus it has no true value. The only way you could ask, "What's closest to pi?" is if you wanted a number rounded to a certain place. Sorry if I've disappointed you, but it's impossible.

But as a reference, the American education system wants you to use 3.14. If the choice is yours to make (i.e., in your job), then I would recommend using 3.14159, which is pi rounded to the hundred-thousandth place. +++

A common approximation, the integer fraction closest to pi and sufficient in practical problems not needing high accuracy, or as a quick estimate of likely answer, is 22/7. I'm surprised US schools stop at only 2 decimal places, when 3 (i.e. pi = 3.142) is more accurate but just as easy to use; but scientific calculators normally have a pi key to umpteen decimal places anyway.

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π is a transcendental number (if you sit and think about π are you doing transcendental meditation?) which is an irrational number which is not the solution to a polynomial with rational coefficients.

Depending how accurate you want your rational approximation there are various fractions that can be used:

22/7 is 3.142857... which is accurate when rounded to 2 decimal places: 3.14

355/113 is 3.1415929... which is accurate when rounded to 6 decimal places: 3.141593

314159265.../100000000... is as accurate as you want it - for each extra digit of π that you append to the numerator you append an extra zero to the denominator.

For most purposes taking π rounded to 2 decimal places (3.14) is sufficient. If you need greater accuracy, taking it rounded to 6 decimal places (3.141593 ≈ 355/113) will do - it all depends upon the accuracy of the other numbers (measurements) in the calculation.

Computer programming languages with in-built values for π are still limited in their accuracy due to the number of bits used to store π. A single precision floating point value can only store π to about 7 digits, a double-precision to about 11 digits; electronic (hand held) calculators are accurate to about 11 digits.

When working with (irrational) numbers like π, it is often better to see if you can simplify the calculation before reaching for a calculator - as the calculation is done each intermediate result can be rounded with the accumulated rounding affecting the final result - I have seen such a calculation in a test paper where the mark scheme allows for errors in the result which come about through the intermediate rounding, but the actual answer is an exact whole number (if the calculation is simplified before being done the exact answer will be calculated).

Q: Which fraction is the clostest to the actual value of pi?

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One can define an infinite number of fractions to successively approximate pi, and get closer and closer to pi's value. There is no closest fraction to pi. No matter how close the fraction is to pi you can always find one that is closer.

If you're looking at a list under this question in the book, I'm sorry you're not letting me see it, and there's no way I can give you the best answer from that list. My choice for the fraction closest to the actual value of (pi) is 22/7 . It's only about 0.04% wrong.

22/7 No! It's a joke. There is no fraction value for pi. Pi is an irrational number, meaning that it cannot be represented in fractional form.

Because 22/7 is the approximate value of pi as a fraction but the exact value of pi has never been determined.

The value of pi is an irrational number because it cannot be expressed as a fraction

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One can define an infinite number of fractions to successively approximate pi, and get closer and closer to pi's value. There is no closest fraction to pi. No matter how close the fraction is to pi you can always find one that is closer.

If you're looking at a list under this question in the book, I'm sorry you're not letting me see it, and there's no way I can give you the best answer from that list. My choice for the fraction closest to the actual value of (pi) is 22/7 . It's only about 0.04% wrong.

22/7 No! It's a joke. There is no fraction value for pi. Pi is an irrational number, meaning that it cannot be represented in fractional form.

the fraction 22/7 is often used as an approximation for the value of pi. it is off from the actual value by about 0.04 percent (1 in 2500). This would be like measuring a football field and being off by about 1.5 inches on your measurement. The fraction 355/113 is amazingly close, better than 1 part in 10 million

It is not practical to work with the actual value of pi, because there is no actual value of pi. We all know that pi more or less equals 3.14159265 . . . but the number of decimal points in pi never ends. 3.14159 is extremely precise, and works for most uses.

Because 22/7 is the approximate value of pi as a fraction but the exact value of pi has never been determined.

The value of pi is an irrational number because it cannot be expressed as a fraction

It is an irrational number such as the value of pi

One can define an infinite number of fractions to successively approximate pi, and get closer and closer to pi's value. There is no closest fraction to pi. No matter how close the fraction is to pi you can always find one that is closer

The value of pi is found by dividing the circumference of a circle by its diameter and pi is an irrational number which means it can not be expressed as a fraction.

The value of pi is an irrational number. Pi is the ratio of the circumference of a circle to the circle's diameter. Also, π is a transcendental number.

A number that can't be expressed as a fraction such as the value of pi.