C) Evaluate $46.8 + 3.06 + 2.4 + 0.09$ And Give The Answer Correct To 3 Significant Figures.
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Introduction
In mathematics, evaluating the sum of decimal numbers is a fundamental operation that requires attention to detail and a clear understanding of the rules of arithmetic. In this article, we will evaluate the sum of four decimal numbers: 46.8, 3.06, 2.4, and 0.09. We will follow a step-by-step approach to ensure accuracy and precision in our calculations.
The Problem
The problem requires us to evaluate the sum of the following decimal numbers:
Step 1: Add the Numbers
To evaluate the sum, we will start by adding the numbers from left to right. We will begin with the first two numbers: 46.8 and 3.06.
Adding 46.8 and 3.06
When we add 46.8 and 3.06, we get:
Adding 49.86 and 2.4
Next, we will add 49.86 and 2.4:
Adding 52.26 and 0.09
Finally, we will add 52.26 and 0.09:
Step 2: Round the Answer to 3 Significant Figures
The final answer should be rounded to 3 significant figures. To do this, we will look at the fourth decimal place, which is 5 in this case. Since the fourth decimal place is greater than or equal to 5, we will round up the third decimal place.
Rounding 52.35 to 3 Significant Figures
When we round 52.35 to 3 significant figures, we get:
Conclusion
In this article, we evaluated the sum of four decimal numbers: 46.8, 3.06, 2.4, and 0.09. We followed a step-by-step approach to ensure accuracy and precision in our calculations. The final answer, rounded to 3 significant figures, is 52.4.
Frequently Asked Questions
Q: What is the correct order of operations when adding decimal numbers?
A: The correct order of operations is to add the numbers from left to right.
Q: How do I round a decimal number to 3 significant figures?
A: To round a decimal number to 3 significant figures, look at the fourth decimal place. If it is greater than or equal to 5, round up the third decimal place.
Q: What is the importance of rounding decimal numbers to 3 significant figures?
A: Rounding decimal numbers to 3 significant figures is important in scientific and engineering applications where precision is crucial.
Summary
In this article, we evaluated the sum of four decimal numbers: 46.8, 3.06, 2.4, and 0.09. We followed a step-by-step approach to ensure accuracy and precision in our calculations. The final answer, rounded to 3 significant figures, is 52.4. We also discussed the importance of rounding decimal numbers to 3 significant figures in scientific and engineering applications.
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Introduction
In our previous article, we evaluated the sum of four decimal numbers: 46.8, 3.06, 2.4, and 0.09. We followed a step-by-step approach to ensure accuracy and precision in our calculations. In this article, we will provide a Q&A guide to help you understand the concepts and techniques involved in evaluating the sum of decimal numbers.
Q&A
Q: What is the correct order of operations when adding decimal numbers?
A: The correct order of operations is to add the numbers from left to right. This means that you should start by adding the first two numbers, then add the result to the third number, and finally add the result to the fourth number.
Q: How do I add decimal numbers with different numbers of decimal places?
A: When adding decimal numbers with different numbers of decimal places, you should line up the decimal points and add the numbers as usual. If the numbers have different numbers of decimal places, you can add zeros to the right of the decimal point to make them the same length.
Q: What is the importance of rounding decimal numbers to 3 significant figures?
A: Rounding decimal numbers to 3 significant figures is important in scientific and engineering applications where precision is crucial. It helps to eliminate unnecessary digits and provide a more accurate representation of the data.
Q: How do I round a decimal number to 3 significant figures?
A: To round a decimal number to 3 significant figures, look at the fourth decimal place. If it is greater than or equal to 5, round up the third decimal place. If it is less than 5, round down the third decimal place.
Q: What is the difference between rounding to 3 significant figures and rounding to 3 decimal places?
A: Rounding to 3 significant figures means that you are rounding the number to 3 digits that are significant, or meaningful, in the context of the problem. Rounding to 3 decimal places means that you are rounding the number to 3 digits after the decimal point.
Q: Can I use a calculator to evaluate the sum of decimal numbers?
A: Yes, you can use a calculator to evaluate the sum of decimal numbers. However, it's always a good idea to double-check your calculations by hand to ensure accuracy.
Q: What are some common mistakes to avoid when evaluating the sum of decimal numbers?
A: Some common mistakes to avoid when evaluating the sum of decimal numbers include:
- Not lining up the decimal points correctly
- Not adding the numbers from left to right
- Not rounding the answer to the correct number of significant figures
- Not checking the calculations for accuracy
Conclusion
In this article, we provided a Q&A guide to help you understand the concepts and techniques involved in evaluating the sum of decimal numbers. We discussed the correct order of operations, how to add decimal numbers with different numbers of decimal places, and the importance of rounding decimal numbers to 3 significant figures. We also covered some common mistakes to avoid when evaluating the sum of decimal numbers.
Frequently Asked Questions
Q: What is the correct way to write a decimal number?
A: The correct way to write a decimal number is to use a period (.) to separate the whole number part from the fractional part.
Q: How do I convert a decimal number to a fraction?
A: To convert a decimal number to a fraction, you can use a calculator or a conversion chart.
Q: What is the difference between a decimal number and a percentage?
A: A decimal number is a number that has a decimal point, while a percentage is a number that represents a proportion of 100.
Summary
In this article, we provided a Q&A guide to help you understand the concepts and techniques involved in evaluating the sum of decimal numbers. We discussed the correct order of operations, how to add decimal numbers with different numbers of decimal places, and the importance of rounding decimal numbers to 3 significant figures. We also covered some common mistakes to avoid when evaluating the sum of decimal numbers.