What is 15.212828... as a Fraction?

15.2128 equals 1506079900 as a fraction.

How do you turn 15.2128 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.2128 repeating into a fraction, begin writing this simple equation:

n = 15.2128 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (28) and 2 digits in the non-repeating part (21). Multiply both sides by 10⁴ = 10000.

10000 × n = 152128.28 (equation 2)

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

10000 × n = 152128.28
  100 × n = 15.2128
 9900 × n = 150607

n = 1506079900 (answer)

15.2128 = 1506079900 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 1506079900 is also equal to 1521079900 when expressed as a mixed number.

The repeating decimal 15.2128 (vinculum notation) has a repeated block length of 2. It is also represented as 15.21282828... (ellipsis notation) which equals approximately 15.212828282828 (decimal approximation)(*).

The recurring decimal 15.2128 can be written as a ratio of two integers having 150607 as the numerator and 9900 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.