What is 10.01538153815381538... as a Fraction?

10.1538 equals 50071949995 as a fraction.

How do you turn 10.1538 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.1538 repeating into a fraction, begin writing this simple equation:

n = 10.1538 (equation 1)

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

10000 × n = 101538.1538 (equation 2)

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

10000 × n = 101538.1538
    1 × n = 10.1538
 9999 × n = 101528

n = 50071949995 (answer)

10.1538 = 50071949995 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 50071949995 is also equal to 1076949995 when expressed as a mixed number.

The repeating decimal 10.1538 (vinculum notation) has a repeated block length of 4. It is also represented as 10.153815381538... (ellipsis notation) which equals approximately 10.15381538153815381538 (decimal approximation)(*).

The recurring decimal 10.1538 can be written as a ratio of two integers having 500719 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.