What is 16.67171... as a Fraction?

16.671 equals 3301198 as a fraction.

How do you turn 16.671 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.671 repeating into a fraction, begin writing this simple equation:

n = 16.671 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (71) and 1 digit in the non-repeating part (6). Multiply both sides by 10³ = 1000.

1000 × n = 16671.71 (equation 2)

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

1000 × n = 16671.71
  10 × n = 16.671
 990 × n = 16505

16505990 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 = 16505990 = 16505 ÷ 5990 ÷ 5 = 3301198. So,

16.671 = 3301198 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 3301198 is also equal to 16133198 when expressed as a mixed number.

The repeating decimal 16.671 (vinculum notation) has a repeated block length of 2. It is also represented as 16.6717171... (ellipsis notation) which equals approximately 16.67171717171 (decimal approximation)(*).

The recurring decimal 16.671 can be written as a ratio of two integers having 3301 as the numerator and 198 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.