What is 14.13555... as a Fraction?

14.135 equals 6361450 as a fraction.

How do you turn 14.135 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.135 repeating into a fraction, begin writing this simple equation:

n = 14.135 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (5) and 2 digits in the non-repeating part (13). Multiply both sides by 10³ = 1000.

1000 × n = 14135.5 (equation 2)

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

1000 × n = 14135.5
 100 × n = 14.135
 900 × n = 12722

12722900 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 = 12722900 = 12722 ÷ 2900 ÷ 2 = 6361450. So,

14.135 = 6361450 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 6361450 is also equal to 1461450 when expressed as a mixed number.

The repeating decimal 14.135 (vinculum notation) has a repeated block length of 1. It is also represented as 14.13555... (ellipsis notation) which equals approximately 14.1355555 (decimal approximation)(*).

The recurring decimal 14.135 can be written as a ratio of two integers having 6361 as the numerator and 450 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.