What is 39.733... as a Fraction?

39.73 equals 59615 as a fraction.

How do you turn 39.73 repeating into a fraction?

Detailed Answer:

Step 1: To convert 39.73 repeating into a fraction, begin writing this simple equation:

n = 39.73 (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 = 3973.3 (equation 2)

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

100 × n = 3973.3
 10 × n = 39.73
 90 × n = 3576

357690 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 = 357690 = 3576 ÷ 690 ÷ 6 = 59615. So,

39.73 = 59615 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 59615 is also equal to 391115 when expressed as a mixed number.

The repeating decimal 39.73 (vinculum notation) has a repeated block length of 1. It is also represented as 39.7333... (ellipsis notation) which equals approximately 39.733333 (decimal approximation)(*).

The recurring decimal 39.73 can be written as a ratio of two integers having 596 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.