Alright, let's work through this step-by-step to convert the given fraction [tex]\(\frac{29}{44}\%\)[/tex] to a decimal value and round it to the nearest hundred-thousandth.
### Step 1: Convert the Fraction to a Percentage
To convert the fraction [tex]\(\frac{29}{44}\)[/tex] to a percentage, follow these steps:
1. Divide the numerator by the denominator:
[tex]\[
\frac{29}{44} \approx 0.6590909090909091
\][/tex]
2. Convert the result to a percentage by multiplying by 100:
[tex]\[
0.6590909090909091 \times 100 \approx 65.9090909090909\%
\][/tex]
### Step 2: Convert the Percentage to a Decimal Value
The percentage we computed is approximately 65.9090909090909%. To express this as a decimal value, divide by 100:
[tex]\[
65.9090909090909\% \div 100 \approx 0.6590909090909091
\][/tex]
### Step 3: Round the Decimal Value
We need to round this decimal value [tex]\(0.6590909090909091\)[/tex] to the nearest hundred-thousandth. The hundred-thousandth place is the fifth digit to the right of the decimal point:
1. Identify the digit in the hundred-thousandth place: In [tex]\(0.6590909090909091\)[/tex], the digit in the hundred-thousandth place is `9`.
2. Look at the digit immediately to the right: The digit to the right of the fifth place is `0`.
Since the digit immediately to the right is less than 5, we do not need to round up the hundred-thousandth place digit. Therefore, the rounded value remains:
[tex]\[
0.65909
\][/tex]
### Summary
So, converting [tex]\(\frac{29}{44}\%\)[/tex] to a decimal value and rounding to the nearest hundred-thousandth, we get:
[tex]\[
\frac{29}{44} \% = 0.65909
\][/tex]
