What is 77.23222... as a Fraction?

77.232 equals 69509900 as a fraction.

How do you turn 77.232 repeating into a fraction?

Detailed Answer:

Step 1: To convert 77.232 repeating into a fraction, begin writing this simple equation:

n = 77.232 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 2 digits in the non-repeating part (23). Multiply both sides by 10³ = 1000.

1000 × n = 77232.2 (equation 2)

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

1000 × n = 77232.2
 100 × n = 77.232
 900 × n = 69509

n = 69509900 (answer)

77.232 = 69509900 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 69509900 is also equal to 77209900 when expressed as a mixed number.

The repeating decimal 77.232 (vinculum notation) has a repeated block length of 1. It is also represented as 77.23222... (ellipsis notation) which equals approximately 77.2322222 (decimal approximation)(*).

The recurring decimal 77.232 can be written as a ratio of two integers having 69509 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.