To find the decimal equivalent of the fraction \( \frac{7}{8} \) rounded to two significant figures, let's go through the steps in detail. ### Step 1: Convert the Fraction to Decimal To convert the fraction \( \frac{7}{8} \) into a decimal, we perform the division of 7 by 8. \[ 7 \div 8 = 0.875 \] ### Step 2: Rounding to Two Significant Figures Now that we have the decimal \( 0.875 \), we need to round it to two significant figures. **Significant figures** are the digits that carry meaning contributing to its precision. In the number \( 0.875 \): - The first significant figure is \( 8 \). - The second significant figure is \( 7 \). - The third significant figure is \( 5 \). To round \( 0.875 \) to two significant figures, we look at the third significant figure (which is \( 5 \)). According to rounding rules: - If the digit after the last significant figure (in this case, the third digit) is 5 or greater, we round up the last significant figure. Since the third digit is \( 5 \), we round up the second significant figure \( 7 \) to \( 8 \). Thus, rounding \( 0.875 \) to two significant figures gives us: \[ 0.88 \] ### Final Answer The decimal equivalent of the fraction \( \frac{7}{8} \) rounded to two significant figures is **C. 0.88**. ### Explanation of Other Options - **A. 0.86**: This option is incorrect because it does not round \( 0.875 \) correctly. It is lower than the correct rounded value. - **B. 0.87**: This option is also incorrect. While it is closer than option A, it still does not round \( 0.875 \) correctly. The correct rounding leads to \( 0.88 \). - **D. 0.89**: This option is incorrect as it rounds \( 0.875 \) up too much. The correct rounding only increases the second significant figure from \( 7 \) to \( 8 \), not to \( 9 \). ### Summary of Key Points - The decimal equivalent of \( \frac{7}{8} \) is \( 0.875 \). - Rounding \( 0.875 \) to two significant figures results in \( 0.88 \). - Significant figures are important for determining how to round numbers correctly. - Always check the digit immediately after the last significant figure to decide whether to round up or down. This thorough understanding of converting fractions to decimals and rounding will help you in similar problems in the future!