To determine the total mass of the two powders and record it to the appropriate number of significant figures, follow these steps:
1. Identify the masses: We have two given masses:
- The first mass is 10.10 grams.
- The second mass is 3.0 grams.
2. Add the masses: Sum the given masses to find the total mass.
[tex]\[
10.10 \, \text{g} + 3.0 \, \text{g} = 13.10 \, \text{g}
\][/tex]
3. Determine the correct number of significant figures: When adding or subtracting numbers, the result should be recorded to the least number of decimal places in the numbers being combined. Here:
- The first mass (10.10 g) has two decimal places.
- The second mass (3.0 g) has one decimal place.
Therefore, the total mass should be recorded to one decimal place, matching the least precise measurement.
4. Round the total mass appropriately: The calculated total mass of 13.10 grams should be rounded to one decimal place.
[tex]\[
13.10 \, \text{g} \rightarrow 13.1 \, \text{g}
\][/tex]
So the total mass of the powders, recorded to the appropriate number of significant figures, is:
[tex]\[
\boxed{13.1 \, \text{g}}
\][/tex]
