What is 0.4857142857142857142857142857142857142... as a Fraction?

0.4857142 equals 1735 as a fraction.

How do you turn 0.4857142 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.4857142 repeating into a fraction, begin writing this simple equation:

n = 0.4857142 (equation 1)

Step 2: Notice that there are 6 digits in the repeating block (857142) and 1 digit in the non-repeating part (4). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 4857142.857142 (equation 2)

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

10000000 × n = 4857142.857142
      10 × n = 0.4857142
 9999990 × n = 4857138

48571389999990 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 285714 (the GCF - greatest common factor).

n = 48571389999990 = 4857138 ÷ 2857149999990 ÷ 285714 = 1735. So,

0.4857142 = 1735 as the lowest possible fraction.

The repeating decimal 0.4857142 (vinculum notation) has a repeated block length of 6. It is also represented as 0.4857142857142857142... (ellipsis notation) which equals approximately 0.4857142857142857142857142857142 (decimal approximation)(*).

The recurring decimal 0.4857142 can be written as a ratio of two integers having 17 as the numerator and 35 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.