To solve the problem of writing the decimal 0.832 as both a percent and a simplified fraction, follow these steps:
### Converting 0.832 to a Percent
1. Understand the conversion: To convert a decimal to a percent, you multiply it by 100.
[tex]\( 0.832 \times 100 = 83.2 \)[/tex]
2. Write the result: Therefore, 0.832 as a percent is [tex]\( 83.2 \% \)[/tex].
### Converting 0.832 to a Fraction
1. Write the decimal as a fraction: The decimal 0.832 can be initially written as [tex]\( \frac{832}{1000} \)[/tex].
2. Simplify the fraction: To simplify [tex]\( \frac{832}{1000} \)[/tex], find the greatest common divisor (GCD) of 832 and 1000 and divide both the numerator and the denominator by this number. In this case, the GCD of 832 and 1000 is 8.
[tex]\[
\frac{832 \div 8}{1000 \div 8} = \frac{104}{125}
\][/tex]
3. Verify the simplified fraction: Confirm that [tex]\( \frac{104}{125} \)[/tex] is in simplest form. There are no common factors between 104 and 125 other than 1.
Therefore, the simplified fraction form of 0.832 is [tex]\( \frac{104}{125} \)[/tex].
### Final Answer
Converting 0.832 to both a percent and a simplified fraction gives us:
[tex]\[ 83.2\% \text{ and } \frac{104}{125} \][/tex]
So, the correct option is:
[tex]\[ 83.2 \% \text{ and } \frac{104}{125} \][/tex]
