What is 0.7307307307... as a Fraction?

0.7307 equals 730999 as a fraction.

How do you turn 0.7307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.7307 repeating into a fraction, begin writing this simple equation:

n = 0.7307 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (307) and 1 digit in the non-repeating part (7). Multiply both sides by 10⁴ = 10000.

10000 × n = 7307.307 (equation 2)

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

10000 × n = 7307.307
   10 × n = 0.7307
 9990 × n = 7300

73009990 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 10 (the GCF - greatest common factor).

n = 73009990 = 7300 ÷ 109990 ÷ 10 = 730999. So,

0.7307 = 730999 as the lowest possible fraction.

The repeating decimal 0.7307 (vinculum notation) has a repeated block length of 3. It is also represented as 0.7307307307... (ellipsis notation) which equals approximately 0.7307307307307307 (decimal approximation)(*).

The recurring decimal 0.7307 can be written as a ratio of two integers having 730 as the numerator and 999 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.