To express [tex]\( 0.832 \)[/tex] as a percent and as a simplified fraction, follow these steps:
1. Convert the decimal to a percentage:
The decimal [tex]\( 0.832 \)[/tex] can be converted to a percentage by multiplying by 100.
[tex]\[ 0.832 \times 100 = 83.2 \% \][/tex]
2. Convert the decimal to a fraction and simplify:
We express [tex]\( 0.832 \)[/tex] as a fraction by recognizing that [tex]\( 0.832 \)[/tex] is equivalent to:
[tex]\[ \frac{832}{1000} \][/tex]
Next, we simplify this fraction. To do so, we find the greatest common divisor (GCD) of 832 and 1000, which is 8. We divide both the numerator and the denominator by their GCD.
[tex]\[ \frac{832 \div 8}{1000 \div 8} = \frac{104}{125} \][/tex]
Now we have [tex]\( 0.832 \)[/tex] as a simplified fraction.
So, combining both the percentage and the simplified fraction, the correct representation of [tex]\( 0.832 \)[/tex] is:
[tex]\[ 83.2 \% \][/tex]
and
[tex]\[ \frac{104}{125} \][/tex]
Thus, the correct option from the given choices is:
[tex]\[ 83.2 \% \quad \text{and} \quad \frac{104}{125} \][/tex]
