What is 14.7142142142... as a Fraction?

14.7142 equals 293991998 as a fraction.

How do you turn 14.7142 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.7142 repeating into a fraction, begin writing this simple equation:

n = 14.7142 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (142) and 1 digit in the non-repeating part (7). Multiply both sides by 10⁴ = 10000.

10000 × n = 147142.142 (equation 2)

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

10000 × n = 147142.142
   10 × n = 14.7142
 9990 × n = 146995

1469959990 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 5 (the GCF - greatest common factor).

n = 1469959990 = 146995 ÷ 59990 ÷ 5 = 293991998. So,

14.7142 = 293991998 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 293991998 is also equal to 1414271998 when expressed as a mixed number.

The repeating decimal 14.7142 (vinculum notation) has a repeated block length of 3. It is also represented as 14.7142142142... (ellipsis notation) which equals approximately 14.7142142142142142 (decimal approximation)(*).

The recurring decimal 14.7142 can be written as a ratio of two integers having 29399 as the numerator and 1998 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.