What is 20.1888... as a Fraction?

20.18 equals 181790 as a fraction.

How do you turn 20.18 repeating into a fraction?

Detailed Answer:

Step 1: To convert 20.18 repeating into a fraction, begin writing this simple equation:

n = 20.18 (equation 1)

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

100 × n = 2018.8 (equation 2)

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

100 × n = 2018.8
 10 × n = 20.18
 90 × n = 1817

n = 181790 (answer)

20.18 = 181790 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 181790 is also equal to 201790 when expressed as a mixed number.

The repeating decimal 20.18 (vinculum notation) has a repeated block length of 1. It is also represented as 20.1888... (ellipsis notation) which equals approximately 20.188888 (decimal approximation)(*).

The recurring decimal 20.18 can be written as a ratio of two integers having 1817 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.