What is 54.25555... as a Fraction?

54.255 equals 488390 as a fraction.

How do you turn 54.255 repeating into a fraction?

Detailed Answer:

Step 1: To convert 54.255 repeating into a fraction, begin writing this simple equation:

n = 54.255 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5) and 2 digits in the non-repeating part (25). Multiply both sides by 10³ = 1000.

1000 × n = 54255.5 (equation 2)

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

1000 × n = 54255.5
 100 × n = 54.255
 900 × n = 48830

48830900 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 10 (the GCF - greatest common factor).

n = 48830900 = 48830 ÷ 10900 ÷ 10 = 488390. So,

54.255 = 488390 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 488390 is also equal to 542390 when expressed as a mixed number.

The repeating decimal 54.255 (vinculum notation) has a repeated block length of 1. It is also represented as 54.25555... (ellipsis notation) which equals approximately 54.2555555 (decimal approximation)(*).

The recurring decimal 54.255 can be written as a ratio of two integers having 4883 as the numerator and 90 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.