What is 11.75222... as a Fraction?

11.752 equals 10577900 as a fraction.

How do you turn 11.752 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.752 repeating into a fraction, begin writing this simple equation:

n = 11.752 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 2 digits in the non-repeating part (75). Multiply both sides by 10³ = 1000.

1000 × n = 11752.2 (equation 2)

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

1000 × n = 11752.2
 100 × n = 11.752
 900 × n = 10577

n = 10577900 (answer)

11.752 = 10577900 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 10577900 is also equal to 11677900 when expressed as a mixed number.

The repeating decimal 11.752 (vinculum notation) has a repeated block length of 1. It is also represented as 11.75222... (ellipsis notation) which equals approximately 11.7522222 (decimal approximation)(*).

The recurring decimal 11.752 can be written as a ratio of two integers having 10577 as the numerator and 900 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.