What is 0.275714257142571425714257142... as a Fraction?

0.2757142 equals 5514231999980 as a fraction.

How do you turn 0.2757142 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.2757142 repeating into a fraction, begin writing this simple equation:

n = 0.2757142 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (57142) and 2 digits in the non-repeating part (27). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 2757142.57142 (equation 2)

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

10000000 × n = 2757142.57142
     100 × n = 0.2757142
 9999900 × n = 2757115

27571159999900 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 5 (the GCF - greatest common factor).

n = 27571159999900 = 2757115 ÷ 59999900 ÷ 5 = 5514231999980. So,

0.2757142 = 5514231999980 as the lowest possible fraction.

The repeating decimal 0.2757142 (vinculum notation) has a repeated block length of 5. It is also represented as 0.27571425714257142... (ellipsis notation) which equals approximately 0.275714257142571425714257142 (decimal approximation)(*).

The recurring decimal 0.2757142 can be written as a ratio of two integers having 551423 as the numerator and 1999980 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.