What is 20.518181818... as a Fraction?

20.518 equals 2257110 as a fraction.

How do you turn 20.518 repeating into a fraction?

Detailed Answer:

Step 1: To convert 20.518 repeating into a fraction, begin writing this simple equation:

n = 20.518 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (18) and 1 digit in the non-repeating part (5). Multiply both sides by 10³ = 1000.

1000 × n = 20518.18 (equation 2)

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

1000 × n = 20518.18
  10 × n = 20.518
 990 × n = 20313

20313990 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 9 (the GCF - greatest common factor).

n = 20313990 = 20313 ÷ 9990 ÷ 9 = 2257110. So,

20.518 = 2257110 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 2257110 is also equal to 2057110 when expressed as a mixed number.

The repeating decimal 20.518 (vinculum notation) has a repeated block length of 2. It is also represented as 20.5181818... (ellipsis notation) which equals approximately 20.51818181818 (decimal approximation)(*).

The recurring decimal 20.518 can be written as a ratio of two integers having 2257 as the numerator and 110 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.