To determine the correct decimal representation of the fraction \( \frac{7}{16} \) rounded to three significant figures, we will follow a step-by-step approach. ### Step 1: Convert the Fraction to Decimal First, we need to convert the fraction \( \frac{7}{16} \) into its decimal form. This can be done by performing the division of 7 by 16. \[ 7 \div 16 = 0.4375 \] ### Step 2: Rounding to Three Significant Figures Now that we have the decimal representation \( 0.4375 \), we need to round it to three significant figures. **Significant figures** are the digits in a number that contribute to its precision. In the number \( 0.4375 \): - The first significant figure is 4. - The second significant figure is 3. - The third significant figure is 7. To round to three significant figures, we look at the fourth digit (which is 5 in this case). According to rounding rules: - If the digit after the last significant figure (the fourth digit) is 5 or greater, we round up the last significant figure. - If it is less than 5, we leave the last significant figure as it is. Since the fourth digit is 5, we round up the third significant figure (7) to 8. Thus, rounding \( 0.4375 \) to three significant figures gives us: \[ 0.438 \] ### Conclusion: Correct Option The correct decimal representation of the fraction \( \frac{7}{16} \) rounded to three significant figures is **B. 0.438**. ### Step 3: Explanation of Other Options Now, let's analyze the other options to understand why they are incorrect or weaker: - **Option A: 0.437** - This option is incorrect because it does not round up the last significant figure. The correct rounding should yield 0.438, not 0.437. - **Option C: 0.440** - This option is incorrect because it incorrectly rounds the number up to 0.440. The last significant figure (7) should not be rounded up to 0.440 since the correct rounding is to 0.438. - **Option D: 0.435** - This option is incorrect as it rounds down the number too much. The correct rounding from 0.4375 should not lead to 0.435, as it fails to account for the 5 in the fourth decimal place. ### Summary of Key Points - The fraction \( \frac{7}{16} \) converts to the decimal 0.4375. - Rounding to three significant figures involves looking at the fourth digit; since it is 5, we round up the last significant figure. - The correct answer is **B. 0.438**. - Other options either do not round correctly or misinterpret the rounding rules. This thorough understanding of the conversion and rounding process will help you tackle similar problems in the future!