What is 57.555... as a Fraction?

57.5 equals 5189 as a fraction.

How do you turn 57.5 repeating into a fraction?

Detailed Answer:

Step 1: To convert 57.5 repeating into a fraction, begin writing this simple equation:

n = 57.5 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5), so multiply both sides by 10¹ = 10.

10 × n = 575.5 (equation 2)

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

10 × n = 575.5
 1 × n = 57.5
 9 × n = 518

n = 5189 (answer)

57.5 = 5189 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 5189 is also equal to 5759 when expressed as a mixed number.

The repeating decimal 57.5 (vinculum notation) has a repeated block length of 1. It is also represented as 57.555... (ellipsis notation) which equals approximately 57.55555 (decimal approximation)(*).

The recurring decimal 57.5 can be written as a ratio of two integers having 518 as the numerator and 9 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.