What is 20.32828... as a Fraction?

20.328 equals 4025198 as a fraction.

How do you turn 20.328 repeating into a fraction?

Detailed Answer:

Step 1: To convert 20.328 repeating into a fraction, begin writing this simple equation:

n = 20.328 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (28) and 1 digit in the non-repeating part (3). Multiply both sides by 10³ = 1000.

1000 × n = 20328.28 (equation 2)

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

1000 × n = 20328.28
  10 × n = 20.328
 990 × n = 20125

20125990 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 5 (the GCF - greatest common factor).

n = 20125990 = 20125 ÷ 5990 ÷ 5 = 4025198. So,

20.328 = 4025198 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 4025198 is also equal to 2065198 when expressed as a mixed number.

The repeating decimal 20.328 (vinculum notation) has a repeated block length of 2. It is also represented as 20.3282828... (ellipsis notation) which equals approximately 20.32828282828 (decimal approximation)(*).

The recurring decimal 20.328 can be written as a ratio of two integers having 4025 as the numerator and 198 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.