What is 0.10030303030303... as a Fraction?

0.1003 equals 3313300 as a fraction.

How do you turn 0.1003 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1003 repeating into a fraction, begin writing this simple equation:

n = 0.1003 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (03) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁴ = 10000.

10000 × n = 1003.03 (equation 2)

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

10000 × n = 1003.03
  100 × n = 0.1003
 9900 × n = 993

9939900 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 = 9939900 = 993 ÷ 39900 ÷ 3 = 3313300. So,

0.1003 = 3313300 as the lowest possible fraction.

The repeating decimal 0.1003 (vinculum notation) has a repeated block length of 2. It is also represented as 0.10030303... (ellipsis notation) which equals approximately 0.100303030303 (decimal approximation)(*).

The recurring decimal 0.1003 can be written as a ratio of two integers having 331 as the numerator and 3300 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.