What is 14.110888... as a Fraction?

14.1108 equals 634994500 as a fraction.

How do you turn 14.1108 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.1108 repeating into a fraction, begin writing this simple equation:

n = 14.1108 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 3 digits in the non-repeating part (110). Multiply both sides by 10⁴ = 10000.

10000 × n = 141108.8 (equation 2)

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

10000 × n = 141108.8
 1000 × n = 14.1108
 9000 × n = 126998

1269989000 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 = 1269989000 = 126998 ÷ 29000 ÷ 2 = 634994500. So,

14.1108 = 634994500 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 634994500 is also equal to 144994500 when expressed as a mixed number.

The repeating decimal 14.1108 (vinculum notation) has a repeated block length of 1. It is also represented as 14.110888... (ellipsis notation) which equals approximately 14.11088888 (decimal approximation)(*).

The recurring decimal 14.1108 can be written as a ratio of two integers having 63499 as the numerator and 4500 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.