What is 3.26230230230... as a Fraction?

3.26230 equals 8147624975 as a fraction.

How do you turn 3.26230 repeating into a fraction?

Detailed Answer:

Step 1: To convert 3.26230 repeating into a fraction, begin writing this simple equation:

n = 3.26230 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (230) and 2 digits in the non-repeating part (26). Multiply both sides by 10⁵ = 100000.

100000 × n = 326230.230 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

100000 × n = 326230.230
   100 × n = 3.26230
 99900 × n = 325904

32590499900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 4 (the GCF - greatest common factor).

n = 32590499900 = 325904 ÷ 499900 ÷ 4 = 8147624975. So,

3.26230 = 8147624975 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 8147624975 is also equal to 3655124975 when expressed as a mixed number.

The repeating decimal 3.26230 (vinculum notation) has a repeated block length of 3. It is also represented as 3.26230230230... (ellipsis notation) which equals approximately 3.26230230230230230 (decimal approximation)(*).

The recurring decimal 3.26230 can be written as a ratio of two integers having 81476 as the numerator and 24975 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.