What is 14.428571428571428571428571428571428571... as a Fraction?

14.428571 equals 1017 as a fraction.

How do you turn 14.428571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.428571 repeating into a fraction, begin writing this simple equation:

n = 14.428571 (equation 1)

Step 2: Notice that there are 6 digits in the repeating block (428571), so multiply both sides by 10⁶ = 1000000.

1000000 × n = 14428571.428571 (equation 2)

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

1000000 × n = 14428571.428571
      1 × n = 14.428571
 999999 × n = 14428557

14428557999999 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 142857 (the GCF - greatest common factor).

n = 14428557999999 = 14428557 ÷ 142857999999 ÷ 142857 = 1017. So,

14.428571 = 1017 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 1017 is also equal to 1437 when expressed as a mixed number.

The repeating decimal 14.428571 (vinculum notation) has a repeated block length of 6. It is also represented as 14.428571428571428571... (ellipsis notation) which equals approximately 14.428571428571428571428571428571 (decimal approximation)(*).

The recurring decimal 14.428571 can be written as a ratio of two integers having 101 as the numerator and 7 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.