What is 336.33333... as a Fraction?

336.333 equals 10093 as a fraction.

How do you turn 336.333 repeating into a fraction?

Detailed Answer:

Step 1: To convert 336.333 repeating into a fraction, begin writing this simple equation:

n = 336.333 (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 = 336333.3 (equation 2)

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

1000 × n = 336333.3
 100 × n = 336.333
 900 × n = 302700

302700900 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 = 302700900 = 302700 ÷ 300900 ÷ 300 = 10093. So,

336.333 = 10093 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 10093 is also equal to 33613 when expressed as a mixed number.

The repeating decimal 336.333 (vinculum notation) has a repeated block length of 1. It is also represented as 336.33333... (ellipsis notation) which equals approximately 336.3333333 (decimal approximation)(*).

The recurring decimal 336.333 can be written as a ratio of two integers having 1009 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.