What is 16.78383838383... as a Fraction?

16.783 equals 8308495 as a fraction.

How do you turn 16.783 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.783 repeating into a fraction, begin writing this simple equation:

n = 16.783 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (83) and 1 digit in the non-repeating part (7). Multiply both sides by 10³ = 1000.

1000 × n = 16783.83 (equation 2)

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

1000 × n = 16783.83
  10 × n = 16.783
 990 × n = 16616

16616990 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 = 16616990 = 16616 ÷ 2990 ÷ 2 = 8308495. So,

16.783 = 8308495 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 8308495 is also equal to 16388495 when expressed as a mixed number.

The repeating decimal 16.783 (vinculum notation) has a repeated block length of 2. It is also represented as 16.7838383... (ellipsis notation) which equals approximately 16.78383838383 (decimal approximation)(*).

The recurring decimal 16.783 can be written as a ratio of two integers having 8308 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.