What is 127.333... as a Fraction?

127.3 equals 3823 as a fraction.

How do you turn 127.3 repeating into a fraction?

Detailed Answer:

Step 1: To convert 127.3 repeating into a fraction, begin writing this simple equation:

n = 127.3 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3), so multiply both sides by 10¹ = 10.

10 × n = 1273.3 (equation 2)

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

10 × n = 1273.3
 1 × n = 127.3
 9 × n = 1146

11469 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 3 (the GCF - greatest common factor).

n = 11469 = 1146 ÷ 39 ÷ 3 = 3823. So,

127.3 = 3823 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 3823 is also equal to 12713 when expressed as a mixed number.

The repeating decimal 127.3 (vinculum notation) has a repeated block length of 1. It is also represented as 127.333... (ellipsis notation) which equals approximately 127.33333 (decimal approximation)(*).

The recurring decimal 127.3 can be written as a ratio of two integers having 382 as the numerator and 3 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.