Final answer:
The repeating decimal 5.066666... can be written as 56/9
Step-by-step explanation:
The repeating decimal 5.066666... can be written as a fraction. To convert a repeating decimal to a fraction, we let 'x' represent the repeating part and 'n' represent the number of digits in the repeating part. In this case, 'x' would be 0.6 and 'n' would be 1. We multiply 'x' by 10^n and subtract 'x' to get a numerator. The denominator is obtained by multiplying 10^n by 10^n and subtracting 1. Simplifying the fraction gives us.
5.066666... = 56/9
Learn more about Converting repeating decimals to fractions