Convert any Arbitrary Decimal Value into a (neater) pi fraction

[programmerBlack]

I was working on a problem that asked me to solve the equation (not needed here) for the angle. I successfully did so, and was asked to select from multiple choice answers. The problem was, the decimal angle that I came out with (in radians) was correct, but the available answers were in the form: [MATH](n * pi / m)[/MATH].

How would I go about converting a decimal value say (0.1308) to the form [MATH](n * pi / m)[/MATH]?

Thanks in advance.

 

[Otis]

… decimal angle … was correct, but the available answers were in the form: [MATH](n * pi / m)[/MATH].
How would I go about converting a decimal value say (0.1308) to the form [MATH](n * pi / m)[/MATH]?

Hello programmerBlack. Given the approximation 0.1308 for \(\frac{n}{m} \pi\), we can estimate n/m.

n/m ∙ Pi ≈ 0.1308

Divide each side by Pi

n/m ≈ 0.0416349

That's about 4/100 (1/25 reduced), or about 42/1000 (21/500 reduced), or about 416/10000 (26/625 reduced), or about 4163/100000, or keep going (until you get as close as you like).

If you're interested in obtaining the exact value of n/m in your posted exercise, then you need to work the exercise using exact numbers (no decimal approximations or rounding in your steps). If the "available" choices were not available to see before you started the exercise, then the exercise ought to have told you in advance that exact answers are required.

?

 

[Dr.Peterson]

I was working on a problem that asked me to solve the equation (not needed here) for the angle. I successfully did so, and was asked to select from multiple choice answers. The problem was, the decimal angle that I came out with (in radians) was correct, but the available answers were in the form: [MATH](n * pi / m)[/MATH].

How would I go about converting a decimal value say (0.1308) to the form [MATH](n * pi / m)[/MATH]?

I think you do need to show us the problem you are solving. If they want exact fractional answers, then I would expect that there is a way to get them without going through decimals. But we can't help you do that without seeing the problem.

Now, there are ways to find the closest fraction (with small numerator and denominator) to a give approximate decimal; Excel lets you format a cell that way, and it tells me your number is close to 1/24 pi (0.13089969 -- I suspect you rounded inappropriately). But that's not the best way to go.