What is 0.20230230230... as a Fraction?

0.20230 equals 20219990 as a fraction.

How do you turn 0.20230 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.20230 repeating into a fraction, begin writing this simple equation:

n = 0.20230 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (230) and 2 digits in the non-repeating part (20). Multiply both sides by 10⁵ = 100000.

100000 × n = 20230.230 (equation 2)

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

100000 × n = 20230.230
   100 × n = 0.20230
 99900 × n = 20210

2021099900 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 10 (the GCF - greatest common factor).

n = 2021099900 = 20210 ÷ 1099900 ÷ 10 = 20219990. So,

0.20230 = 20219990 as the lowest possible fraction.

The repeating decimal 0.20230 (vinculum notation) has a repeated block length of 3. It is also represented as 0.20230230230... (ellipsis notation) which equals approximately 0.20230230230230230 (decimal approximation)(*).

The recurring decimal 0.20230 can be written as a ratio of two integers having 2021 as the numerator and 9990 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.