What is 13.117222... as a Fraction?

13.1172 equals 236111800 as a fraction.

How do you turn 13.1172 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.1172 repeating into a fraction, begin writing this simple equation:

n = 13.1172 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 3 digits in the non-repeating part (117). Multiply both sides by 10⁴ = 10000.

10000 × n = 131172.2 (equation 2)

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

10000 × n = 131172.2
 1000 × n = 13.1172
 9000 × n = 118055

1180559000 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 = 1180559000 = 118055 ÷ 59000 ÷ 5 = 236111800. So,

13.1172 = 236111800 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 236111800 is also equal to 132111800 when expressed as a mixed number.

The repeating decimal 13.1172 (vinculum notation) has a repeated block length of 1. It is also represented as 13.117222... (ellipsis notation) which equals approximately 13.11722222 (decimal approximation)(*).

The recurring decimal 13.1172 can be written as a ratio of two integers having 23611 as the numerator and 1800 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.