How do you find a continued fraction?

How do you find a continued fraction?

To calculate a continued fraction representation of a number r, write down the integer part (technically the floor) of r. Subtract this integer part from r. If the difference is 0, stop; otherwise find the reciprocal of the difference and repeat.

How do you write pi as a continued fraction?

Continued Fraction Expansion: π = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, 1, 2, 1, 1, 12, 1, 1, 1, 3, 1, 1, 8, 1, 1, 2, 1, 6, 1, 1, 5, 2, 2, 3, 1, 2, 4, 4, 16, 1, 161, 45, 1, 22, 1, 2, 2, 1,… ]

Why are continued fractions important?

In mathematics, regular continued fractions play an important role in representing real numbers, and have a rich general theory touching on a variety of topics in number theory. Moreover, generalized continued fractions have important and interesting applications in complex analysis.

How do you turn 10.5 into a fraction?

Step 2: Multiply both top and bottom by 10 for every number after the decimal point: As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So, 10.5/100 = (10.5 x 10)/(100 x 10) = 105/1000.

What are consecutive fractions?

A consecutive fraction is a number written as a series of alternating multiplicative inverses and integer addition operators. Consecutive fractions are studied in the number theory branch of mathematics. Consecutive fractions are also known as continued fractions and extended fractions.

Who invented continued fractions?

The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument.