To convert the decimal 12.8 to a fraction, we can follow these steps:
-
Write 12.8 as a mixed number: \[ 12.8 = 12 + 0.8 \]
-
Convert 0.8 into a fraction: \[ 0.8 = \frac{8}{10} \] We can simplify this: \[ \frac{8}{10} = \frac{4}{5} \quad (\text{dividing both the numerator and the denominator by 2}) \]
-
Now, we can combine the whole number and the simplified fraction: \[ 12.8 = 12 + \frac{4}{5} = \frac{12 \cdot 5 + 4}{5} = \frac{60 + 4}{5} = \frac{64}{5} \]
Thus, 12.8 as a fraction in simplest form is \[ \frac{64}{5} \]
Since this answer does not match any of the provided options, it's possible you might be looking for a specific format. However, if we break down the options given:
- 12810 is not a fraction.
- 12 Start Fraction 8 over 10 End Fraction: This simplifies to \(\frac{64}{5}\).
- 1245 is not a fraction.
- 12 Start Fraction 4 over 5 End Fraction: This simplifies to \(12 + \frac{4}{5}\), which also leads us back to \(\frac{64}{5}\).
- 12225 is not a fraction.
- 128 is not a fraction.
Given that, while the direct simplified form is \(\frac{64}{5}\), the most relevant options based on mixed-number representation are 12 Start Fraction 4 over 5 End Fraction because this aligns with our process of simplification leading to the correct total representation of the decimal as a fraction.
Thus, the correct answer reflecting the conversion of 12.8 into a fraction in the simplest form is 12 Start Fraction 4 over 5 End Fraction—which leads indirectly to \(\frac{64}{5}\).