Chapter 1: Problem 80
What is the total mass, in grams, of a dessert containing \(137.25 \mathrm{~g}\) of vanilla ice cream, \(84 \mathrm{~g}\) of fudge sauce, and \(43.7 \mathrm{~g}\) of nuts?
Short Answer
Expert verified
264.95 grams
Step by step solution
Over 22 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Unit Conversion
Understanding unit conversion is important in chemistry for accurate calculations. In the given problem, the mass of all ingredients is already in grams. Sometimes, different units like kilograms (kg) or milligrams (mg) may be used and need conversion.
To convert from kg to g, multiply by 1000. For example, if you have 0.5 kg of an ingredient, multiplying by 1000 gives you 500 g. Knowing when to convert units ensures you can accurately proceed with addition and other operations.
- 1 kg = 1000 g
- 1 g = 1000 mg
To convert from kg to g, multiply by 1000. For example, if you have 0.5 kg of an ingredient, multiplying by 1000 gives you 500 g. Knowing when to convert units ensures you can accurately proceed with addition and other operations.
Addition of Masses
Adding masses involves summing up the values of different ingredients to find a total. In the example, we have:
Vanilla ice cream: 137.25 g
Fudge sauce: 84 g
Nuts: 43.7 g
Add these values step by step. Arrange them neatly in an addition equation:
\( 137.25 \text{g} + 84 \text{g} + 43.7 \text{g} \)
Perform the addition, starting from the rightmost digit. Align decimal points to ensure the addition is accurate.
\(137.25 + 84 + 43.7 = 264.95 \)
So, the total mass of the dessert is 264.95 grams.
Fudge sauce: 84 g
Nuts: 43.7 g
Add these values step by step. Arrange them neatly in an addition equation:
\( 137.25 \text{g} + 84 \text{g} + 43.7 \text{g} \)
Perform the addition, starting from the rightmost digit. Align decimal points to ensure the addition is accurate.
\(137.25 + 84 + 43.7 = 264.95 \)
So, the total mass of the dessert is 264.95 grams.
Significant Figures
Significant figures (sig figs) are crucial in reporting the precision of your calculations. When performing operations like addition, your final answer should be rounded based on the number with the least decimal places. In our problem:
\(137.25 \) has 5 significant figures
\(84 \) has 2 significant figures
\(43.7 \) has 3 significant figures
When summing these numbers: \(137.25 + 84 + 43.7 = 264.95 \)
The result should honor the least number of decimal places, which is from 84 (no decimal places).
Therefore, the final result should be rounded to 265 grams, ensuring all measurements align with the appropriate precision. This ensures the reliability and consistency of your calculations.
\(137.25 \) has 5 significant figures
\(84 \) has 2 significant figures
\(43.7 \) has 3 significant figures
When summing these numbers: \(137.25 + 84 + 43.7 = 264.95 \)
The result should honor the least number of decimal places, which is from 84 (no decimal places).
Therefore, the final result should be rounded to 265 grams, ensuring all measurements align with the appropriate precision. This ensures the reliability and consistency of your calculations.
