What is 128.8333... as a Fraction?

128.83 equals 7736 as a fraction.

How do you turn 128.83 repeating into a fraction?

Detailed Answer:

Step 1: To convert 128.83 repeating into a fraction, begin writing this simple equation:

n = 128.83 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 1 digit in the non-repeating part (8). Multiply both sides by 10² = 100.

100 × n = 12883.3 (equation 2)

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

100 × n = 12883.3
 10 × n = 128.83
 90 × n = 11595

1159590 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 15 (the GCF - greatest common factor).

n = 1159590 = 11595 ÷ 1590 ÷ 15 = 7736. So,

128.83 = 7736 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 7736 is also equal to 12856 when expressed as a mixed number.

The repeating decimal 128.83 (vinculum notation) has a repeated block length of 1. It is also represented as 128.8333... (ellipsis notation) which equals approximately 128.833333 (decimal approximation)(*).

The recurring decimal 128.83 can be written as a ratio of two integers having 773 as the numerator and 6 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.