What is 18.12323... as a Fraction?

18.123 equals 8971495 as a fraction.

How do you turn 18.123 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.123 repeating into a fraction, begin writing this simple equation:

n = 18.123 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (23) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 18123.23 (equation 2)

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

1000 × n = 18123.23
  10 × n = 18.123
 990 × n = 17942

17942990 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 = 17942990 = 17942 ÷ 2990 ÷ 2 = 8971495. So,

18.123 = 8971495 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 8971495 is also equal to 1861495 when expressed as a mixed number.

The repeating decimal 18.123 (vinculum notation) has a repeated block length of 2. It is also represented as 18.1232323... (ellipsis notation) which equals approximately 18.12323232323 (decimal approximation)(*).

The recurring decimal 18.123 can be written as a ratio of two integers having 8971 as the numerator and 495 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.