To find the decimal equivalent of the fraction \( \frac{7}{16} \) and round it to three significant figures, we will follow a systematic approach. ### Step 1: Convert the Fraction to Decimal To convert the fraction \( \frac{7}{16} \) into a decimal, we can perform the division of 7 by 16. 1. **Long Division Method**: - Divide 7 by 16. - Since 7 is less than 16, we start with 0. - We can add a decimal point and a zero to 7, making it 70. - Now, divide 70 by 16: - 16 goes into 70 four times (since \( 16 \times 4 = 64 \)). - Subtract 64 from 70, which gives us 6. - Bring down another 0, making it 60. - 16 goes into 60 three times (since \( 16 \times 3 = 48 \)). - Subtract 48 from 60, which gives us 12. - Bring down another 0, making it 120. - 16 goes into 120 seven times (since \( 16 \times 7 = 112 \)). - Subtract 112 from 120, which gives us 8. - Bring down another 0, making it 80. - 16 goes into 80 five times (since \( 16 \times 5 = 80 \)). - Subtract 80 from 80, which gives us 0. So, the long division gives us: \[ \frac{7}{16} = 0.4375 \] ### Step 2: Rounding to Three Significant Figures Now that we have the decimal \( 0.4375 \), we need to round it to three significant figures. 1. **Identifying Significant Figures**: - The first three significant figures in \( 0.4375 \) are 4, 3, and 7. - The next digit (the fourth significant figure) is 5. 2. **Rounding Rule**: - If the digit following the last significant figure (in this case, 7) is 5 or greater, we round up the last significant figure. - Since the fourth digit is 5, we round up the 7 to 8. Thus, rounding \( 0.4375 \) to three significant figures gives us: \[ 0.438 \] ### Conclusion: Correct Option The correct option is **B. 0.438**. ### Explanation of Other Options - **Option A: 0.437**: This option is incorrect because it does not round up the last significant figure (7) when the next digit (5) indicates that it should be rounded up. - **Option C: 0.439**: This option is incorrect because it incorrectly rounds the last significant figure (7) to 9 instead of 8. - **Option D: 0.440**: This option is incorrect because it rounds the last significant figure (7) to 0, which is not accurate based on the rounding rules. ### Revision Summary - To convert a fraction to a decimal, perform long division. - Identify significant figures correctly when rounding. - Apply rounding rules: round up if the next digit is 5 or greater. - The decimal equivalent of \( \frac{7}{16} \) rounded to three significant figures is \( 0.438 \).