Convert Decimal 0.800 to Simplified Fraction Form

To convert the decimal 0.800 into a fraction, follow these steps:

• Step 1: Recognize the placement of the decimal. Since 0.800 has three decimal places, consider it as $\frac{800}{1000}$.
• Step 2: Simplify the fraction $\frac{800}{1000}$. The greatest common divisor (GCD) of 800 and 1000 is 200. Divide both numerator and denominator by 200 to simplify:

$\frac{800}{1000} = \frac{800 \div 200}{1000 \div 200} = \frac{4}{5}$.

The fraction $\frac{4}{5}$ is the simplest form of $\frac{800}{1000}$.

Since 0.800 can be understood in terms of place value, the equivalent fraction is $\frac{8}{10}$ as well:

• Step 3: Simplify the alternative fraction $\frac{8}{10}$:

$\frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5}$.

Both fractions reduce to the same simplest form: $\frac{4}{5}$.

Looking at the provided choices, Choices 1 ($\frac{8}{10}$) and 2 ($\frac{800}{1000}$) are both correct representations of the same value as they simplify to the fraction $\frac{4}{5}$.

Thus, according to the choices, the correct answer is: Answers (a) and (b) are correct.