What is 103.2111... as a Fraction?

103.21 equals 928990 as a fraction.

How do you turn 103.21 repeating into a fraction?

Detailed Answer:

Step 1: To convert 103.21 repeating into a fraction, begin writing this simple equation:

n = 103.21 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (1) and 1 digit in the non-repeating part (2). Multiply both sides by 10² = 100.

100 × n = 10321.1 (equation 2)

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

100 × n = 10321.1
 10 × n = 103.21
 90 × n = 9289

n = 928990 (answer)

103.21 = 928990 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 928990 is also equal to 1031990 when expressed as a mixed number.

The repeating decimal 103.21 (vinculum notation) has a repeated block length of 1. It is also represented as 103.2111... (ellipsis notation) which equals approximately 103.211111 (decimal approximation)(*).

The recurring decimal 103.21 can be written as a ratio of two integers having 9289 as the numerator and 90 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.