0.53333333333 into a fraction

To convert the decimal 0.53333333333 into a fraction, follow these steps:

1. Identify the place value of the decimal. In this case, it's in the tenth place, so the decimal can be written over 10: 0.53333333333/1.

2. Because the decimal repeats, we recognize this as a recurring decimal. To convert a recurring decimal into a fraction, we use the formula: a/b = (10^n * x - x) / (10^n - 1), where n is the number of repeating digits and x is the repeating decimal.

3. In this case, n = 1 (as there is one repeating digit, 3) and x = 0.53333333333. Substituting these values into the formula gives us: (10 * 0.53333333333 - 0.53333333333) / (10 - 1).

4. Simplifying this gives us: 5.3333333333 - 0.53333333333 = 4.8 and 10 - 1 = 9. So, the fraction is 4.8/9.

5. To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor. In this case, the greatest common divisor of 4.8 and 9 is 0.6. So, 4.8 ÷ 0.6 = 8 and 9 ÷ 0.6 = 15.

6. Therefore, the fraction form of 0.53333333333 is 8/15.