What is 0.33252525... as a Fraction?

0.3325 equals 8232475 as a fraction.

How do you turn 0.3325 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.3325 repeating into a fraction, begin writing this simple equation:

n = 0.3325 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (25) and 2 digits in the non-repeating part (33). Multiply both sides by 10⁴ = 10000.

10000 × n = 3325.25 (equation 2)

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

10000 × n = 3325.25
  100 × n = 0.3325
 9900 × n = 3292

32929900 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 4 (the GCF - greatest common factor).

n = 32929900 = 3292 ÷ 49900 ÷ 4 = 8232475. So,

0.3325 = 8232475 as the lowest possible fraction.

The repeating decimal 0.3325 (vinculum notation) has a repeated block length of 2. It is also represented as 0.33252525... (ellipsis notation) which equals approximately 0.332525252525 (decimal approximation)(*).

The recurring decimal 0.3325 can be written as a ratio of two integers having 823 as the numerator and 2475 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.