What is 106.8333... as a Fraction?

106.83 equals 6416 as a fraction.

How do you turn 106.83 repeating into a fraction?

Detailed Answer:

Step 1: To convert 106.83 repeating into a fraction, begin writing this simple equation:

n = 106.83 (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 = 10683.3 (equation 2)

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

100 × n = 10683.3
 10 × n = 106.83
 90 × n = 9615

961590 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 = 961590 = 9615 ÷ 1590 ÷ 15 = 6416. So,

106.83 = 6416 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 6416 is also equal to 10656 when expressed as a mixed number.

The repeating decimal 106.83 (vinculum notation) has a repeated block length of 1. It is also represented as 106.8333... (ellipsis notation) which equals approximately 106.833333 (decimal approximation)(*).

The recurring decimal 106.83 can be written as a ratio of two integers having 641 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.