What is 10.021212121... as a Fraction?

10.21 equals 3307330 as a fraction.

How do you turn 10.21 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.21 repeating into a fraction, begin writing this simple equation:

n = 10.21 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (21), so multiply both sides by 10² = 100.

100 × n = 1021.21 (equation 2)

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

100 × n = 1021.21
  1 × n = 10.21
 99 × n = 1011

101199 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 = 101199 = 1011 ÷ 399 ÷ 3 = 3307330. So,

10.21 = 3307330 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 3307330 is also equal to 107330 when expressed as a mixed number.

The repeating decimal 10.21 (vinculum notation) has a repeated block length of 2. It is also represented as 10.212121... (ellipsis notation) which equals approximately 10.2121212121 (decimal approximation)(*).

The recurring decimal 10.21 can be written as a ratio of two integers having 3307 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.