To determine which decimal representation accurately approximates the fraction \( \frac{7}{16} \) to three significant figures, we first need to convert the fraction into its decimal form. ### Step 1: Convert the Fraction to Decimal To convert \( \frac{7}{16} \) into a decimal, we perform the division of 7 by 16: \[ 7 \div 16 = 0.4375 \] ### Step 2: Round to Three Significant Figures Now that we have the decimal representation \( 0.4375 \), we need to round it to three significant figures. The first three significant figures in \( 0.4375 \) are \( 437 \). To round \( 0.4375 \) to three significant figures: - Look at the fourth digit (which is \( 5 \)). - Since \( 5 \) is equal to or greater than \( 5 \), we round up the last significant figure (which is \( 7 \)) by \( 1 \). Thus, rounding \( 0.4375 \) gives us: \[ 0.438 \] ### Step 3: Compare with the Options Now, we need to compare \( 0.438 \) with the provided options: - **A. 0.437**: This is less than \( 0.438 \) and does not round up correctly. - **B. 0.450**: This is greater than \( 0.438 \) and is not a correct approximation. - **C. 0.440**: This is also greater than \( 0.438 \) and does not represent the fraction accurately. - **D. 0.420**: This is significantly less than \( 0.438 \) and is not a correct approximation. ### Conclusion None of the options provided accurately represent \( \frac{7}{16} \) rounded to three significant figures, as the correct rounded value is \( 0.438 \). However, if we were to choose the closest option to \( 0.4375 \) without rounding, option **A (0.437)** is the best choice, even though it is not the correct rounded value. ### Summary of Why Each Option is Incorrect or Weaker - **A. 0.437**: Closest to \( 0.438 \) but does not round correctly. - **B. 0.450**: Too high; does not represent \( \frac{7}{16} \). - **C. 0.440**: Also too high; does not represent \( \frac{7}{16} \). - **D. 0.420**: Significantly lower than \( 0.4375 \); incorrect approximation. ### Revision Summary - Convert fractions to decimals by division. - Round to the required number of significant figures by checking the next digit. - Compare the rounded value with the provided options to find the closest match. - Understand that rounding rules dictate how to adjust the last significant figure based on the next digit.