What is 17.60101... as a Fraction?

17.601 equals 3485198 as a fraction.

How do you turn 17.601 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.601 repeating into a fraction, begin writing this simple equation:

n = 17.601 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (01) and 1 digit in the non-repeating part (6). Multiply both sides by 10³ = 1000.

1000 × n = 17601.01 (equation 2)

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

1000 × n = 17601.01
  10 × n = 17.601
 990 × n = 17425

17425990 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 = 17425990 = 17425 ÷ 5990 ÷ 5 = 3485198. So,

17.601 = 3485198 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 3485198 is also equal to 17119198 when expressed as a mixed number.

The repeating decimal 17.601 (vinculum notation) has a repeated block length of 2. It is also represented as 17.6010101... (ellipsis notation) which equals approximately 17.60101010101 (decimal approximation)(*).

The recurring decimal 17.601 can be written as a ratio of two integers having 3485 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.