What is 12.5307307307... as a Fraction?

12.5307 equals 625914995 as a fraction.

How do you turn 12.5307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.5307 repeating into a fraction, begin writing this simple equation:

n = 12.5307 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (307) and 1 digit in the non-repeating part (5). Multiply both sides by 10⁴ = 10000.

10000 × n = 125307.307 (equation 2)

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

10000 × n = 125307.307
   10 × n = 12.5307
 9990 × n = 125182

1251829990 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 2 (the GCF - greatest common factor).

n = 1251829990 = 125182 ÷ 29990 ÷ 2 = 625914995. So,

12.5307 = 625914995 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 625914995 is also equal to 1226514995 when expressed as a mixed number.

The repeating decimal 12.5307 (vinculum notation) has a repeated block length of 3. It is also represented as 12.5307307307... (ellipsis notation) which equals approximately 12.5307307307307307 (decimal approximation)(*).

The recurring decimal 12.5307 can be written as a ratio of two integers having 62591 as the numerator and 4995 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.