What is 1.0571428571428571428571428571428571428... as a Fraction?

1.571428 equals 3735 as a fraction.

How do you turn 1.571428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.571428 repeating into a fraction, begin writing this simple equation:

n = 1.571428 (equation 1)

Step 2: Notice that there are 6 digits in the repeating block (571428), so multiply both sides by 10⁶ = 1000000.

1000000 × n = 1571428.571428 (equation 2)

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

1000000 × n = 1571428.571428
      1 × n = 1.571428
 999999 × n = 1571427

1571427999999 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 = 1571427999999 = 1571427 ÷ 142857999999 ÷ 142857 = 3735. So,

1.571428 = 3735 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 3735 is also equal to 1235 when expressed as a mixed number.

The repeating decimal 1.571428 (vinculum notation) has a repeated block length of 6. It is also represented as 1.571428571428571428... (ellipsis notation) which equals approximately 1.571428571428571428571428571428 (decimal approximation)(*).

The recurring decimal 1.571428 can be written as a ratio of two integers having 37 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.