What is 0.10230230230... as a Fraction?

0.10230 equals 5114995 as a fraction.

How do you turn 0.10230 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.10230 repeating into a fraction, begin writing this simple equation:

n = 0.10230 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (230) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁵ = 100000.

100000 × n = 10230.230 (equation 2)

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

100000 × n = 10230.230
   100 × n = 0.10230
 99900 × n = 10220

1022099900 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 20 (the GCF - greatest common factor).

n = 1022099900 = 10220 ÷ 2099900 ÷ 20 = 5114995. So,

0.10230 = 5114995 as the lowest possible fraction.

The repeating decimal 0.10230 (vinculum notation) has a repeated block length of 3. It is also represented as 0.10230230230... (ellipsis notation) which equals approximately 0.10230230230230230 (decimal approximation)(*).

The recurring decimal 0.10230 can be written as a ratio of two integers having 511 as the numerator and 4995 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.