What is 10.12828... as a Fraction?

10.128 equals 10027990 as a fraction.

How do you turn 10.128 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.128 repeating into a fraction, begin writing this simple equation:

n = 10.128 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (28) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 10128.28 (equation 2)

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

1000 × n = 10128.28
  10 × n = 10.128
 990 × n = 10027

n = 10027990 (answer)

10.128 = 10027990 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 10027990 is also equal to 10127990 when expressed as a mixed number.

The repeating decimal 10.128 (vinculum notation) has a repeated block length of 2. It is also represented as 10.1282828... (ellipsis notation) which equals approximately 10.12828282828 (decimal approximation)(*).

The recurring decimal 10.128 can be written as a ratio of two integers having 10027 as the numerator and 990 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.