Final answer:
To simplify the expression 2.3 (3 repeating) as a fraction, we convert the repeating decimal into a fraction. Dividing both sides of the equation by 9, we get x = 2.3 (3 repeating) / 9. Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, we get 7/9.
Step-by-step explanation:
To simplify the expression 2.3 (3 repeating), we can convert the repeating decimal into a fraction. Let's call the repeating decimal x. Multiplying x by 10 gives 10x, and subtracting x from 10x gives 9x. So, 10x - x = 9x. Now, we can write the equation: 9x = 2.3 (3 repeating). Solve for x by dividing both sides of the equation by 9: x = 2.3 (3 repeating) / 9.
To simplify the fraction, we can multiply the numerator and denominator by 10 to eliminate the repeating decimal. This gives us: x = (2.3 (3 repeating) * 10) / (9 * 10) = 23.3 / 90. Now, we can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor is 3. Dividing 23.3 by 3 gives us 7.767, and dividing 90 by 3 gives us 30. Therefore, the simplified fraction is 7.767 / 30.
The correct option is d) 7/9.