What is 75.7333... as a Fraction?

75.73 equals 113615 as a fraction.

How do you turn 75.73 repeating into a fraction?

Detailed Answer:

Step 1: To convert 75.73 repeating into a fraction, begin writing this simple equation:

n = 75.73 (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 = 7573.3 (equation 2)

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

100 × n = 7573.3
 10 × n = 75.73
 90 × n = 6816

681690 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 = 681690 = 6816 ÷ 690 ÷ 6 = 113615. So,

75.73 = 113615 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 113615 is also equal to 751115 when expressed as a mixed number.

The repeating decimal 75.73 (vinculum notation) has a repeated block length of 1. It is also represented as 75.7333... (ellipsis notation) which equals approximately 75.733333 (decimal approximation)(*).

The recurring decimal 75.73 can be written as a ratio of two integers having 1136 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.