What is 323.3333... as a Fraction?

323.333 equals 9703 as a fraction.

How do you turn 323.333 repeating into a fraction?

Detailed Answer:

Step 1: To convert 323.333 repeating into a fraction, begin writing this simple equation:

n = 323.333 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (33). Multiply both sides by 10³ = 1000.

1000 × n = 323333.3 (equation 2)

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

1000 × n = 323333.3
 100 × n = 323.333
 900 × n = 291000

291000900 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 300 (the GCF - greatest common factor).

n = 291000900 = 291000 ÷ 300900 ÷ 300 = 9703. So,

323.333 = 9703 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 9703 is also equal to 32313 when expressed as a mixed number.

The repeating decimal 323.333 (vinculum notation) has a repeated block length of 1. It is also represented as 323.33333... (ellipsis notation) which equals approximately 323.3333333 (decimal approximation)(*).

The recurring decimal 323.333 can be written as a ratio of two integers having 970 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.