Question

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

264.95 grams

Step-by-step solution

Identify the masses

The masses of the ingredients are given as follows: Vanilla ice cream: 137.25 grams, Fudge sauce: 84 grams, Nuts: 43.7 grams.

Set up the addition

Place all the masses in an addition equation: \( 137.25 \text{g} + 84 \text{g} + 43.7 \text{g} \).

Perform the addition

Add the values together: \( 137.25 + 84 + 43.7 = 264.95 \).

State the total mass

The total mass is \( 264.95 \text{ grams} \).

Key concepts

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.

• 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.

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.