What is 14.102666... as a Fraction?

14.1026 equals 10577750 as a fraction.

How do you turn 14.1026 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.1026 repeating into a fraction, begin writing this simple equation:

n = 14.1026 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 3 digits in the non-repeating part (102). Multiply both sides by 10⁴ = 10000.

10000 × n = 141026.6 (equation 2)

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

10000 × n = 141026.6
 1000 × n = 14.1026
 9000 × n = 126924

1269249000 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 12 (the GCF - greatest common factor).

n = 1269249000 = 126924 ÷ 129000 ÷ 12 = 10577750. So,

14.1026 = 10577750 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 10577750 is also equal to 1477750 when expressed as a mixed number.

The repeating decimal 14.1026 (vinculum notation) has a repeated block length of 1. It is also represented as 14.102666... (ellipsis notation) which equals approximately 14.10266666 (decimal approximation)(*).

The recurring decimal 14.1026 can be written as a ratio of two integers having 10577 as the numerator and 750 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.