A volumetric flask contains 100.0 mL of water.

A volumetric flask contains 100.0 mL of water. This volume is added to a beaker containing 175 mL of water. Choose the value that expresses the new total volume of water in the beaker with the correct number of significant figures. A) 275 mL B) 280 mL C) 275.0 mL D) 300 mL E) 275.00 mL

The Correct Answer and Explanation is:

The correct answer is B) 280 mL.

Here’s why:

1. Understanding Significant Figures:
   • Significant figures (sig figs) are the digits in a number that contribute to its precision. When performing operations like addition or subtraction, the result should be reported with the same number of decimal places as the measurement with the fewest decimal places.
2. Step 1: Identify the Significant Figures in Each Measurement:
   • The volume in the volumetric flask is 100.0 mL. This measurement has 4 significant figures because the decimal point indicates precision.
   • The volume in the beaker is 175 mL, which has 3 significant figures because there is no decimal point, so we count all the digits.
3. Step 2: Addition of the Volumes:
   • To find the total volume, we add the two measurements together: 100.0 mL+175 mL=275.0 mL100.0 \, \text{mL} + 175 \, \text{mL} = 275.0 \, \text{mL}100.0mL+175mL=275.0mL
   • However, since the least precise measurement (175 mL) has no decimal places, the result must be rounded to the nearest whole number to match the precision of the least precise measurement.
4. Step 3: Rounding the Result:
   • The calculated sum is 275.0 mL, but because we need to express the total volume with the same precision as the least precise measurement (which is 175 mL with 0 decimal places), the result should be rounded to 280 mL.
5. Conclusion:
   • The result is 280 mL, since we round 275.0 mL to 280 mL, ensuring that it matches the precision of the least precise measurement.

Thus, the correct answer is B) 280 mL.