What is 10.07142871428714287142871428... as a Fraction?

10.71428 equals 5035664499995 as a fraction.

How do you turn 10.71428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.71428 repeating into a fraction, begin writing this simple equation:

n = 10.71428 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (71428), so multiply both sides by 10⁵ = 100000.

100000 × n = 1071428.71428 (equation 2)

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

100000 × n = 1071428.71428
     1 × n = 10.71428
 99999 × n = 1071418

n = 5035664499995 (answer)

10.71428 = 5035664499995 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 5035664499995 is also equal to 1035714499995 when expressed as a mixed number.

The repeating decimal 10.71428 (vinculum notation) has a repeated block length of 5. It is also represented as 10.714287142871428... (ellipsis notation) which equals approximately 10.7142871428714287142871428 (decimal approximation)(*).

The recurring decimal 10.71428 can be written as a ratio of two integers having 5035664 as the numerator and 499995 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.