What is the correct number of significant figures resulting from the following calculation? \[ 14.73 \times(9.7+3.35) \]

To determine the correct number of significant figures in the result of the calculation \( 14.73 \times (9.7 + 3.35) \), we need to follow the rules for significant figures in addition and multiplication. 1. **Calculate the sum inside the parentheses:** \[ 9.7 + 3.35 \] - The number \( 9.7 \) has 2 decimal places (the tenths place). - The number \( 3.35 \) has 2 decimal places (the hundredths place). - When adding, the result should be rounded to the least number of decimal places, which is 1 decimal place (from \( 9.7 \)). \[ 9.7 + 3.35 = 13.05 \quad \text{(but rounded to 1 decimal place gives)} \quad 13.1 \] 2. **Now multiply by \( 14.73 \):** \[ 14.73 \times 13.1 \] - The number \( 14.73 \) has 4 significant figures. - The number \( 13.1 \) has 3 significant figures (since it is rounded to 1 decimal place). - When multiplying, the result should be reported with the same number of significant figures as the factor with the least significant figures, which is 3 in this case. 3. **Perform the multiplication:** \[ 14.73 \times 13.1 = 192.763 \] 4. **Round the result to 3 significant figures:** - The number \( 192.763 \) rounded to 3 significant figures is \( 193 \). Thus, the final result of the calculation \( 14.73 \times (9.7 + 3.35) \) should be reported with **3 significant figures**.