What is 333.3833... as a Fraction?

333.383 equals 2000360 as a fraction.

How do you turn 333.383 repeating into a fraction?

Detailed Answer:

Step 1: To convert 333.383 repeating into a fraction, begin writing this simple equation:

n = 333.383 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (38). Multiply both sides by 10³ = 1000.

1000 × n = 333383.3 (equation 2)

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

1000 × n = 333383.3
 100 × n = 333.383
 900 × n = 300045

300045900 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 = 300045900 = 300045 ÷ 15900 ÷ 15 = 2000360. So,

333.383 = 2000360 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 2000360 is also equal to 3332360 when expressed as a mixed number.

The repeating decimal 333.383 (vinculum notation) has a repeated block length of 1. It is also represented as 333.38333... (ellipsis notation) which equals approximately 333.3833333 (decimal approximation)(*).

The recurring decimal 333.383 can be written as a ratio of two integers having 20003 as the numerator and 60 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.