What is 16.81414... as a Fraction?

16.814 equals 8323495 as a fraction.

How do you turn 16.814 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.814 repeating into a fraction, begin writing this simple equation:

n = 16.814 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (14) and 1 digit in the non-repeating part (8). Multiply both sides by 10³ = 1000.

1000 × n = 16814.14 (equation 2)

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

1000 × n = 16814.14
  10 × n = 16.814
 990 × n = 16646

16646990 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 = 16646990 = 16646 ÷ 2990 ÷ 2 = 8323495. So,

16.814 = 8323495 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 8323495 is also equal to 16403495 when expressed as a mixed number.

The repeating decimal 16.814 (vinculum notation) has a repeated block length of 2. It is also represented as 16.8141414... (ellipsis notation) which equals approximately 16.81414141414 (decimal approximation)(*).

The recurring decimal 16.814 can be written as a ratio of two integers having 8323 as the numerator and 495 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.