What is 16.1142142142... as a Fraction?

16.1142 equals 1609819990 as a fraction.

How do you turn 16.1142 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.1142 repeating into a fraction, begin writing this simple equation:

n = 16.1142 (equation 1)

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

10000 × n = 161142.142 (equation 2)

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

10000 × n = 161142.142
   10 × n = 16.1142
 9990 × n = 160981

n = 1609819990 (answer)

16.1142 = 1609819990 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 1609819990 is also equal to 1611419990 when expressed as a mixed number.

The repeating decimal 16.1142 (vinculum notation) has a repeated block length of 3. It is also represented as 16.1142142142... (ellipsis notation) which equals approximately 16.1142142142142142 (decimal approximation)(*).

The recurring decimal 16.1142 can be written as a ratio of two integers having 160981 as the numerator and 9990 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.