Question

*2. sharlas batting average in softball is $0.58\overline{3}$. which fraction represents sharlas batting average? show work to prove your answer.
a. $\frac{5}{8}$
b. $\frac{5}{9}$
c. $\frac{7}{11}$
d. $\frac{7}{12}$
ns.2

Explanation:

Step1: Define the repeating decimal

Let $x = 0.58\overline{3}$, which means $x = 0.58333...$

Step2: Eliminate the repeating part

Multiply $x$ by 100 to shift past non-repeating decimals:
$100x = 58.333...$
Multiply $x$ by 1000 to shift one full repeat:
$1000x = 583.333...$

Step3: Subtract to solve for x

Subtract $100x$ from $1000x$:
$1000x - 100x = 583.333... - 58.333...$
$900x = 525$

Step4: Simplify the fraction

Solve for $x$:
$x = \frac{525}{900}$
Divide numerator and denominator by 75:
$x = \frac{7}{12}$

Step5: Verify with options

Calculate each option:
a. $\frac{5}{8} = 0.625$
b. $\frac{5}{9} \approx 0.555...$
c. $\frac{7}{11} \approx 0.636...$
d. $\frac{7}{12} \approx 0.5833...$

Answer:

d. 7/12