Carry Out The Following Operation And Express The Answer With The Appropriate Number Of Significant Figures.a. $4.3220 - 1.304$
Understanding Significant Figures
Significant figures are an essential concept in mathematics, particularly in numerical calculations. They represent the precision or reliability of a measurement or a calculated value. In this article, we will explore the concept of significant figures and how to apply them in mathematical operations.
What are Significant Figures?
Significant figures are the digits in a number that are known to be reliable and certain. They are used to express the precision of a measurement or a calculated value. The number of significant figures in a value depends on the instrument or method used to obtain the measurement.
Rules for Significant Figures
There are several rules to follow when working with significant figures:
- Non-zero digits are always significant: Any non-zero digit in a number is considered significant.
- Zeros between non-zero digits are significant: Zeros that appear between non-zero digits are also significant.
- Leading zeros are not significant: Zeros that appear at the beginning of a number are not significant.
- Trailing zeros are significant only if the number contains a decimal point: If a number contains a decimal point, trailing zeros are significant. However, if the number does not contain a decimal point, trailing zeros are not significant.
Significant Figures in Addition and Subtraction
When performing addition and subtraction operations, the number of significant figures in the answer is determined by the number with the fewest significant figures.
Example 1: Addition
Suppose we want to add 4.3220 and 1.304. To determine the number of significant figures in the answer, we need to look at the number with the fewest significant figures.
| Number | Significant Figures |
|---|---|
| 4.3220 | 5 |
| 1.304 | 3 |
Since 1.304 has the fewest significant figures (3), the answer will also have 3 significant figures.
4.3220 + 1.304 = 5.626
Example 2: Subtraction
Suppose we want to subtract 1.304 from 4.3220. To determine the number of significant figures in the answer, we need to look at the number with the fewest significant figures.
| Number | Significant Figures |
|---|---|
| 4.3220 | 5 |
| 1.304 | 3 |
Since 1.304 has the fewest significant figures (3), the answer will also have 3 significant figures.
4.3220 - 1.304 = 3.018
Significant Figures in Multiplication and Division
When performing multiplication and division operations, the number of significant figures in the answer is determined by the number with the fewest significant figures.
Example 1: Multiplication
Suppose we want to multiply 4.3220 and 1.304. To determine the number of significant figures in the answer, we need to look at the number with the fewest significant figures.
| Number | Significant Figures |
|---|---|
| 4.3220 | 5 |
| 1.304 | 3 |
Since 1.304 has the fewest significant figures (3), the answer will also have 3 significant figures.
4.3220 × 1.304 = 5.623
Example 2: Division
Suppose we want to divide 4.3220 by 1.304. To determine the number of significant figures in the answer, we need to look at the number with the fewest significant figures.
| Number | Significant Figures |
|---|---|
| 4.3220 | 5 |
| 1.304 | 3 |
Since 1.304 has the fewest significant figures (3), the answer will also have 3 significant figures.
4.3220 ÷ 1.304 = 3.294
Conclusion
Significant figures are an essential concept in mathematics, particularly in numerical calculations. They represent the precision or reliability of a measurement or a calculated value. In this article, we explored the concept of significant figures and how to apply them in mathematical operations. We also discussed the rules for significant figures and how to determine the number of significant figures in the answer for addition, subtraction, multiplication, and division operations.
a.
To determine the number of significant figures in the answer, we need to look at the number with the fewest significant figures.
| Number | Significant Figures |
|---|---|
| 4.3220 | 5 |
| 1.304 | 3 |
Since 1.304 has the fewest significant figures (3), the answer will also have 3 significant figures.
4.3220 - 1.304 = 2.018
Frequently Asked Questions about Significant Figures
Significant figures are an essential concept in mathematics, particularly in numerical calculations. However, many students and professionals may have questions about significant figures. In this article, we will answer some of the most frequently asked questions about significant figures.
Q: What is the purpose of significant figures?
A: The purpose of significant figures is to express the precision or reliability of a measurement or a calculated value. Significant figures help to indicate the level of accuracy in a measurement or calculation.
Q: How do I determine the number of significant figures in a number?
A: To determine the number of significant figures in a number, you need to follow these rules:
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros are not significant.
- Trailing zeros are significant only if the number contains a decimal point.
Q: What is the difference between significant figures and decimal places?
A: Significant figures and decimal places are related but distinct concepts. Decimal places refer to the number of digits after the decimal point in a number. Significant figures, on the other hand, refer to the number of digits that are known to be reliable and certain.
Q: How do I round numbers to the correct number of significant figures?
A: To round numbers to the correct number of significant figures, you need to follow these steps:
- Determine the number of significant figures required.
- Look at the digit immediately to the right of the last significant digit.
- If the digit is 5 or greater, round up the last significant digit.
- If the digit is less than 5, round down the last significant digit.
Q: Can I have a number with more significant figures than the number of decimal places?
A: Yes, you can have a number with more significant figures than the number of decimal places. For example, the number 4.3220 has 5 significant figures, but only 3 decimal places.
Q: How do I handle significant figures in multiplication and division?
A: When performing multiplication and division operations, the number of significant figures in the answer is determined by the number with the fewest significant figures.
Q: Can I have a number with fewer significant figures than the number of decimal places?
A: Yes, you can have a number with fewer significant figures than the number of decimal places. For example, the number 4.32 has 3 significant figures, but 2 decimal places.
Q: How do I handle significant figures in addition and subtraction?
A: When performing addition and subtraction operations, the number of significant figures in the answer is determined by the number with the fewest significant figures.
Q: Can I have a number with the same number of significant figures as the number of decimal places?
A: Yes, you can have a number with the same number of significant figures as the number of decimal places. For example, the number 4.32 has 3 significant figures and 2 decimal places.
Conclusion
Significant figures are an essential concept in mathematics, particularly in numerical calculations. In this article, we answered some of the most frequently asked questions about significant figures. We hope that this article has helped to clarify any confusion about significant figures and how to apply them in mathematical operations.
Common Mistakes to Avoid when Working with Significant Figures
- Not following the rules for significant figures: Make sure to follow the rules for significant figures when determining the number of significant figures in a number.
- Rounding numbers incorrectly: Make sure to round numbers to the correct number of significant figures.
- Not considering the number of decimal places: Make sure to consider the number of decimal places when determining the number of significant figures in a number.
- Not handling significant figures correctly in multiplication and division: Make sure to handle significant figures correctly in multiplication and division operations.
- Not handling significant figures correctly in addition and subtraction: Make sure to handle significant figures correctly in addition and subtraction operations.
By avoiding these common mistakes, you can ensure that you are working with significant figures correctly and accurately.