What is 76.7333... as a Fraction?

76.73 equals 115115 as a fraction.

How do you turn 76.73 repeating into a fraction?

Detailed Answer:

Step 1: To convert 76.73 repeating into a fraction, begin writing this simple equation:

n = 76.73 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 1 digit in the non-repeating part (7). Multiply both sides by 10² = 100.

100 × n = 7673.3 (equation 2)

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

100 × n = 7673.3
 10 × n = 76.73
 90 × n = 6906

690690 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 6 (the GCF - greatest common factor).

n = 690690 = 6906 ÷ 690 ÷ 6 = 115115. So,

76.73 = 115115 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 115115 is also equal to 761115 when expressed as a mixed number.

The repeating decimal 76.73 (vinculum notation) has a repeated block length of 1. It is also represented as 76.7333... (ellipsis notation) which equals approximately 76.733333 (decimal approximation)(*).

The recurring decimal 76.73 can be written as a ratio of two integers having 1151 as the numerator and 15 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.