While cleaning out the lab vials listing the following volumes of unknown liquid waste were discovered:

5.10 mL

1.050 x 102 mL

47.1 x 10-2 mL

In order to dispose of this waste, the total volume must be reported in scientific notation with the correct number of significant figures and the units of milliliters.

[Fill in the blank],
x 10[Fill in the blank],
mL

Question

While cleaning out the lab vials listing the following volumes of unknown liquid waste were discovered:

5.10 mL

1.050 x 102 mL

47.1 x 10-2 mL

In order to dispose of this waste, the total volume must be reported in scientific notation with the correct number of significant figures and the units of milliliters.

[Fill in the blank],
 x 10[Fill in the blank],
 mL

BlackTom AI · Accepted Answer

We start by clearly identifying the task: add the volumes given, then express the total in scientific notation with the correct number of significant figures and units (mL).

First, convert each quantity to a consistent form (in milliliters with their original sig figs preserved):
- 5.10 mL already is in mL with three significant figures; value = 5.10 mL.
- 1.050 x 102 mL means 1.050 times 10^2, which equals 105.0 mL; this maintains four significant figures.
- 47.1 x 10^-2 mL equals 47.1 multiplied by 0.01, which is 0.471 mL; this has three significant figures.

Next, add the three quantities, paying attention to the rules for addition: you align by decimal places and keep the least precise decimal place among the addends.
- 5.10 has two decimal places.
- 105.0 has one decimal place.
- 0.471 has three decimal places.
The sum is 5.10 + 105.0 + 0.471 = 110.571 mL.
Since the least precise decimal place among the addends is one decimal place (from 105.0 mL), you should report the total with one decimal place: 110.6 mL.

Now convert this total to scientific notation: 110.6 mL = 1.106 x 10^2 mL.
Depending on how many significant figures you choose to display in scientific notation, you might round differently:
- To four significant figures: 1.106 x 10^2 mL.
- To three significant figures: 1.11 x 10^2 mL.
- To two significant figures: 1.1 x 10^2 mL.

The provided answers (1.67 for the first blank and 2 for the second blank) would correspond to 1.67 x 10^2 mL = 167 mL, which does not match the computed total 110.6 mL. This suggests a mismatch between the computed sum and the supplied answer key.

If we instead were to force the blanks to match the given key exactly (first blank 1.67, second blank 2), that would indicate reporting 1.67 x 10^2 mL = 167 mL, which is not consistent with the sum of the three volumes as calculated above. The discrepancy highlights the importance of carefully applying addition precision rules and consistent conversions when preparing scientific notation with correct significant figures.

In summary, the correct approach yields a total around 110.6 mL, and the scientific notation would be on the order of 1.11 x 10^2 mL (depending on the desired sig figs), not 1.67 x 10^2 mL. The given answer values appear to mismatch the calculated total based on standard sig fig and decimal place rules.

M2LA F25 Lab Fundamentals I Quiz

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