What is 335.33333... as a Fraction?

335.333 equals 10063 as a fraction.

How do you turn 335.333 repeating into a fraction?

Detailed Answer:

Step 1: To convert 335.333 repeating into a fraction, begin writing this simple equation:

n = 335.333 (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 = 335333.3 (equation 2)

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

1000 × n = 335333.3
 100 × n = 335.333
 900 × n = 301800

301800900 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 = 301800900 = 301800 ÷ 300900 ÷ 300 = 10063. So,

335.333 = 10063 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 10063 is also equal to 33513 when expressed as a mixed number.

The repeating decimal 335.333 (vinculum notation) has a repeated block length of 1. It is also represented as 335.33333... (ellipsis notation) which equals approximately 335.3333333 (decimal approximation)(*).

The recurring decimal 335.333 can be written as a ratio of two integers having 1006 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.