What is 55.1555... as a Fraction?

55.15 equals 248245 as a fraction.

How do you turn 55.15 repeating into a fraction?

Detailed Answer:

Step 1: To convert 55.15 repeating into a fraction, begin writing this simple equation:

n = 55.15 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5) and 1 digit in the non-repeating part (1). Multiply both sides by 10² = 100.

100 × n = 5515.5 (equation 2)

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

100 × n = 5515.5
 10 × n = 55.15
 90 × n = 4964

496490 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 2 (the GCF - greatest common factor).

n = 496490 = 4964 ÷ 290 ÷ 2 = 248245. So,

55.15 = 248245 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 248245 is also equal to 55745 when expressed as a mixed number.

The repeating decimal 55.15 (vinculum notation) has a repeated block length of 1. It is also represented as 55.1555... (ellipsis notation) which equals approximately 55.155555 (decimal approximation)(*).

The recurring decimal 55.15 can be written as a ratio of two integers having 2482 as the numerator and 45 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.