What is 1.42857285728572857... as a Fraction?

1.42857 equals 14284399990 as a fraction.

How do you turn 1.42857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.42857 repeating into a fraction, begin writing this simple equation:

n = 1.42857 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (2857) and 1 digit in the non-repeating part (4). Multiply both sides by 10⁵ = 100000.

100000 × n = 142857.2857 (equation 2)

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

100000 × n = 142857.2857
    10 × n = 1.42857
 99990 × n = 142843

n = 14284399990 (answer)

1.42857 = 14284399990 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 14284399990 is also equal to 14285399990 when expressed as a mixed number.

The repeating decimal 1.42857 (vinculum notation) has a repeated block length of 4. It is also represented as 1.4285728572857... (ellipsis notation) which equals approximately 1.428572857285728572857 (decimal approximation)(*).

The recurring decimal 1.42857 can be written as a ratio of two integers having 142843 as the numerator and 99990 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.