Answer
a) 32.8 mL, 32 mL, 32.73 mL
b) Yes, it is possible for all the breakers to contain the same amount of water. The amount of water in the beakers was measured according to the most precise marking (ex: each marking represents a mL) and then with one number of uncertainty. This fits with significant digit rules because each measurement is marked according to the most precise measurement marking and one uncertain value after.
c) 98 mL
Work Step by Step
answer a:
- beaker 1: The most precise measurement marking on this beaker indicates changes in 1 mL per marking. The volume in the beaker is between the 32 mL and 33 mL marking. According to the significant figure rules, the volume is measured to the lowest number of certainty (32 mL) and with one digit of uncertainty (0.8 mL), making the measured value 32.8 mL. Because this final digit is uncertain, correct answers range from 32.1 mL to 32.9 mL.
- beaker 2: Following the significant digit rules explained above, the volume is measured to the lowest number of certainty (indicated by the smallest mark, which shows 10 mL of water per mark) and to one number of uncertainty. Therefore, the value is 32mL. Acceptable answers range from 30 mL to 39 mL due to the uncertain ones value.
- beaker 3: Following the significant digit rules explained above, the volume is measured to the lowest number of certainty (indicated by the smallest mark, which shows 0.1 mL of water per mark) and to one number of uncertainty. Therefore, the value is 32.73 mL. Acceptable answers range from 32.70 to 32.79 mL due to the final number of uncertainty.
answer b: see explanation in answer
answer c: To find the total amount of water in all three beakers, add the measured amounts of water in each beaker. The total amount is given by 32.8 + 32 + 32.73 mL, which equals 97.53 mL. Due to significant digit rules about addition, the final answer/amount is about 98 mL. To solve addition problems with amounts of different precisions/significant digits, add and show the sum to the same number of significant digits as the least precise amount added. In this case, the lowest number of significant digits is in beaker 2, which only measures to the 10 mL precision. Therefore, the final sum must be in 2 significant digits as the lowest amount recorded (32 mL - beaker 2) was.
