Final answer:
To express 3.4 repeating as a fraction, we can rewrite it as 3 + 0.4 and convert 0.4 to a fraction. The fractional representation of 0.4 is 4/10. Since the decimal repeats, we place the repeating digit(s) (4) over a number of nines equal to the number of repeating digits, resulting in the fraction 4/9.
Step-by-step explanation:
To write 3.4 repeating as a fraction, we can use the concept of repeating decimals. We can rewrite 3.4 as 3 + 0.4. The number 0.4 can be expressed as 4/10. Since the decimal continues to repeat, we can represent it as a fraction by placing the repeating digit(s) (4) over a number of nines equal to the number of repeating digits. In this case, there is one repeating digit, so we divide 4 by 9, resulting in the fraction 4/9.
Learn more about repeating decimals