To write the fraction [tex]\(\frac{41}{13}\)[/tex] as a decimal and round it to the nearest hundredth, follow these steps:
1. Calculate the Decimal Value: First, divide the numerator (41) by the denominator (13). This gives you the decimal value:
[tex]\[
\frac{41}{13} \approx 3.1538461538461537
\][/tex]
2. Round to the Nearest Hundredth: Identify the position of the hundredths place in the decimal (it's the second digit to the right of the decimal point). The digit in the thousandths place (the third digit to the right of the decimal point) determines whether you round up or down:
- In the number 3.1538461538461537, the hundredths place is occupied by '5', and the digit immediately after it is '3'.
- Since '3' is less than 5, you round down, keeping the '5' in the hundredths place.
Therefore, the fraction [tex]\(\frac{41}{13}\)[/tex] as a decimal rounded to the nearest hundredth is approximately:
[tex]\[
\frac{41}{13} \approx 3.15
\][/tex]
