What is 17.223030... as a Fraction?

17.2230 equals 14209825 as a fraction.

How do you turn 17.2230 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.2230 repeating into a fraction, begin writing this simple equation:

n = 17.2230 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (30) and 2 digits in the non-repeating part (22). Multiply both sides by 10⁴ = 10000.

10000 × n = 172230.30 (equation 2)

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

10000 × n = 172230.30
  100 × n = 17.2230
 9900 × n = 170508

1705089900 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 12 (the GCF - greatest common factor).

n = 1705089900 = 170508 ÷ 129900 ÷ 12 = 14209825. So,

17.2230 = 14209825 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 14209825 is also equal to 17184825 when expressed as a mixed number.

The repeating decimal 17.2230 (vinculum notation) has a repeated block length of 2. It is also represented as 17.22303030... (ellipsis notation) which equals approximately 17.223030303030 (decimal approximation)(*).

The recurring decimal 17.2230 can be written as a ratio of two integers having 14209 as the numerator and 825 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.