What is 5.261428514285142851428514285... as a Fraction?

5.2614285 equals 526137599999900 as a fraction.

How do you turn 5.2614285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 5.2614285 repeating into a fraction, begin writing this simple equation:

n = 5.2614285 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (14285) and 2 digits in the non-repeating part (26). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 52614285.14285 (equation 2)

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

10000000 × n = 52614285.14285
     100 × n = 5.2614285
 9999900 × n = 52613759

n = 526137599999900 (answer)

5.2614285 = 526137599999900 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 526137599999900 is also equal to 526142599999900 when expressed as a mixed number.

The repeating decimal 5.2614285 (vinculum notation) has a repeated block length of 5. It is also represented as 5.26142851428514285... (ellipsis notation) which equals approximately 5.261428514285142851428514285 (decimal approximation)(*).

The recurring decimal 5.2614285 can be written as a ratio of two integers having 52613759 as the numerator and 9999900 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.