What is 56.86... as a Fraction?

56.86 equals 85315 as a fraction.

How do you turn 56.86 repeating into a fraction?

Detailed Answer:

Step 1: To convert 56.86 repeating into a fraction, begin writing this simple equation:

n = 56.86 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 1 digit in the non-repeating part (8). Multiply both sides by 10² = 100.

100 × n = 5686.6 (equation 2)

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

100 × n = 5686.6
 10 × n = 56.86
 90 × n = 5118

511890 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 6 (the GCF - greatest common factor).

n = 511890 = 5118 ÷ 690 ÷ 6 = 85315. So,

56.86 = 85315 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 85315 is also equal to 561315 when expressed as a mixed number.

The repeating decimal 56.86 (vinculum notation) has a repeated block length of 1. It is also represented as 56.8666... (ellipsis notation) which equals approximately 56.866666 (decimal approximation)(*).

The recurring decimal 56.86 can be written as a ratio of two integers having 853 as the numerator and 15 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.