What is 2.72307230723072307... as a Fraction?

2.72307 equals 90763333 as a fraction.

How do you turn 2.72307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.72307 repeating into a fraction, begin writing this simple equation:

n = 2.72307 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (2307) and 1 digit in the non-repeating part (7). Multiply both sides by 10⁵ = 100000.

100000 × n = 272307.2307 (equation 2)

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

100000 × n = 272307.2307
    10 × n = 2.72307
 99990 × n = 272280

27228099990 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 30 (the GCF - greatest common factor).

n = 27228099990 = 272280 ÷ 3099990 ÷ 30 = 90763333. So,

2.72307 = 90763333 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 90763333 is also equal to 224103333 when expressed as a mixed number.

The repeating decimal 2.72307 (vinculum notation) has a repeated block length of 4. It is also represented as 2.7230723072307... (ellipsis notation) which equals approximately 2.723072307230723072307 (decimal approximation)(*).

The recurring decimal 2.72307 can be written as a ratio of two integers having 9076 as the numerator and 3333 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.