Calculating Mass: A Step-by-Step Guide

Hey guys! Let's dive into a common physics problem: determining the total mass when you have multiple measurements. In this case, we're looking at a substance with measurements of 37.24 g and 10.3 g. The goal is to find the total mass, and we'll walk through the process step-by-step. Understanding how to handle these calculations is key in any science field, so let's make sure we get it right. This isn't just about adding numbers; it's about understanding significant figures and how they affect the accuracy of your answer. Ready to learn something new? Let's get started!

Understanding the Problem and Key Concepts

Alright, first things first: let's break down what we're dealing with. We've got two mass measurements for the same substance. The first measurement is 37.24 g, and the second is 10.3 g. The plus sign (+) indicates that we need to combine these masses to find the total mass. This seems straightforward, right? Well, it is, but we need to pay close attention to significant figures. Significant figures are the digits in a measurement that contribute to its precision. When you add or subtract measurements, the answer's precision is limited by the least precise measurement. The core concept here is that our final answer can't be more precise than our least precise measurement. For example, if you have a measurement of 10.0 g and another of 10.000 g, your final answer should be around 10.0 g since the first number has only 3 significant figures. So, while basic addition is the core of this calculation, the true trick lies in correctly applying the rules of significant figures. This ensures that the answer is accurate and reflects the precision of our measurements. Let’s make sure we don’t lose any important digits while calculating and reporting the final answer. Ready to jump into the calculation? Let's go!

Significant Figures: The Precision Players

Before we jump into the numbers, let's chat about significant figures. They're super important in science because they tell us how reliable our measurements are. When you measure something, your measuring tool has a certain level of precision. Significant figures reflect that precision. For addition and subtraction, the rule is to look at the decimal places. Your final answer should have the same number of decimal places as the measurement with the fewest decimal places. For example, if you're adding 10.5 g and 2.22 g, your answer should only have one decimal place because 10.5 g has only one decimal place. So, let's keep an eye on those decimal places as we work through the problem. This isn't just about getting the right number; it's about showing that you understand the accuracy of your measurements. Remembering these rules is essential to accurately and meaningfully interpreting scientific data.

Step-by-Step Calculation of the Total Mass

Okay, now for the fun part: doing the actual calculation. We have our two mass measurements: 37.24 g and 10.3 g. Here's how to find the total mass:

1. Add the measurements: First, add the two masses together: 37.24 g + 10.3 g = 47.54 g.
2. Determine the significant figures: Now, the crucial part: we need to consider significant figures. The first measurement (37.24 g) has two decimal places, while the second measurement (10.3 g) has one decimal place. Remember, when adding or subtracting, the answer should have the same number of decimal places as the number with the fewest decimal places. In this case, that's one decimal place.
3. Round the answer: Since our answer (47.54 g) has two decimal places, we need to round it to one decimal place. 47.54 g rounded to one decimal place becomes 47.5 g.

So, the final answer, taking significant figures into account, is 47.5 g. It means that the total mass of the substance is 47.5 g, keeping in mind the accuracy of our measurements. Pretty straightforward, right? It really just involves paying careful attention to detail and remembering the rules for significant figures. Good job, guys!

Writing the Final Answer Correctly

When writing your final answer, always include the units (in this case, grams or "g") to specify what you're measuring. Make sure the number is written clearly, and it reflects the proper number of significant figures. So, for our problem, the correct way to write the answer is: Total mass = 47.5 g. This format shows that you understand the process and have applied the rules correctly. Ensure your answer is easily understood and accurately reflects the precision of your measurements. This practice is crucial in ensuring that your work is scientifically sound. Nice work, you have successfully performed the mass calculation!

Common Mistakes to Avoid

Let’s look at some common pitfalls when solving problems like this. First, forgetting to consider significant figures is a big one. Without this step, your answer might appear correct numerically but will not be scientifically accurate. Second, incorrectly rounding the answer can lead to an imprecise final value. Always double-check your rounding. Third, missing the units is another mistake. Always include the correct units (grams, in this case) to show what you're measuring. By staying alert and focusing on these areas, you can avoid these frequent mistakes and boost the quality of your answers. Pay close attention to each step, and you’ll get it right! That’s it! Great job!

Conclusion: Mastering Mass Calculations

And there you have it, guys! We've successfully calculated the total mass and correctly accounted for significant figures. Remember, practice makes perfect. Keep working on these types of problems, and you'll become a pro at them in no time. The key takeaways from this exercise are understanding how to add measurements, recognizing the importance of significant figures, and knowing how to round your answer correctly. These skills are vital in physics and other scientific fields, so pat yourself on the back! Keep up the excellent work, and always remember to double-check your steps. You got this!