What is 0.6307307307... as a Fraction?

0.6307 equals 63019990 as a fraction.

How do you turn 0.6307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.6307 repeating into a fraction, begin writing this simple equation:

n = 0.6307 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (307) and 1 digit in the non-repeating part (6). Multiply both sides by 10⁴ = 10000.

10000 × n = 6307.307 (equation 2)

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

10000 × n = 6307.307
   10 × n = 0.6307
 9990 × n = 6301

n = 63019990 (answer)

0.6307 = 63019990 as the lowest possible fraction.

The repeating decimal 0.6307 (vinculum notation) has a repeated block length of 3. It is also represented as 0.6307307307... (ellipsis notation) which equals approximately 0.6307307307307307 (decimal approximation)(*).

The recurring decimal 0.6307 can be written as a ratio of two integers having 6301 as the numerator and 9990 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.