What is 0.01538153815381538... as a Fraction?

0.1538 equals 76949995 as a fraction.

How do you turn 0.1538 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.1538 repeating into a fraction, begin writing this simple equation:

n = 0.1538 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (1538), so multiply both sides by 10⁴ = 10000.

10000 × n = 1538.1538 (equation 2)

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

10000 × n = 1538.1538
    1 × n = 0.1538
 9999 × n = 1538

n = 76949995 (answer)

0.1538 = 76949995 as the lowest possible fraction.

The repeating decimal 0.1538 (vinculum notation) has a repeated block length of 4. It is also represented as 0.153815381538... (ellipsis notation) which equals approximately 0.15381538153815381538 (decimal approximation)(*).

The recurring decimal 0.1538 can be written as a ratio of two integers having 769 as the numerator and 49995 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.