What is 20.12424... as a Fraction?

20.124 equals 6641330 as a fraction.

How do you turn 20.124 repeating into a fraction?

Detailed Answer:

Step 1: To convert 20.124 repeating into a fraction, begin writing this simple equation:

n = 20.124 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (24) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 20124.24 (equation 2)

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

1000 × n = 20124.24
  10 × n = 20.124
 990 × n = 19923

19923990 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 3 (the GCF - greatest common factor).

n = 19923990 = 19923 ÷ 3990 ÷ 3 = 6641330. So,

20.124 = 6641330 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 6641330 is also equal to 2041330 when expressed as a mixed number.

The repeating decimal 20.124 (vinculum notation) has a repeated block length of 2. It is also represented as 20.1242424... (ellipsis notation) which equals approximately 20.12424242424 (decimal approximation)(*).

The recurring decimal 20.124 can be written as a ratio of two integers having 6641 as the numerator and 330 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.