Final answer:
Yes, 0.71 (75 repeating) is a rational number because it can be expressed as a fraction.
Step-by-step explanation:
Yes, 0.71 (75 repeating) is a rational number.
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. In this case, we can write the repeating decimal 0.71 (75 repeating) as a fraction. Let x = 0.71 (75 repeating). Multiply both sides by 100 to eliminate the repeating decimal: 100x = 71.7575...
Subtracting the original equation from the second equation, we get 99x = 71. That means x = 71/99, which is a fraction and therefore a rational number.