Carry the correct number of significant figures

Oct 13, 2025 by pynkocean.com 99 views

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Introduction

When dealing with numerical values, it's essential to understand the concept of significant figures. Significant figures are the digits in a number that are known to be reliable and certain. In this article, we will explore the number $$8.90 \times 10^6$$ and determine the number of significant figures it contains.

Understanding Significant Figures

Significant figures are a way to express the precision of a measurement or a calculated value. They are used to indicate the reliability of a number and to avoid confusion when performing calculations. The number of significant figures in a value depends on the measurement or calculation method used to obtain it.

Counting Significant Figures

To count the significant figures in a number, we need to follow a set of rules:

Non-zero digits: All non-zero digits are significant.
Zeros between non-zero digits: Zeros between non-zero digits are significant.
Leading zeros: Leading zeros are not significant.
Trailing zeros: Trailing zeros are significant only if the number contains a decimal point.

Analyzing the Given Number

Now, let's apply the rules to the given number $$8.90 \times 10^6$$.

The first digit, 8, is a non-zero digit, so it's significant.
The second digit, 9, is also a non-zero digit, so it's significant.
The third digit, 0, is a zero between non-zero digits, so it's significant.
The fourth digit, 9, is a non-zero digit, so it's significant.
The fifth digit, 0, is a trailing zero, but it's not significant because the number does not contain a decimal point.
The exponent, $$10^6$$, is not a significant figure.

Conclusion

Based on the analysis, the number $$8.90 \times 10^6$$ has 4 significant figures.

Significance of Significant Figures

Significant figures are crucial in mathematics and science because they help us understand the precision of a measurement or a calculated value. When performing calculations, it's essential to carry the correct number of significant figures to avoid errors.

Example Use Case

Suppose we have a measurement of 8.90 meters, and we want to calculate the area of a rectangle with a length of 10 meters. We would need to carry the correct number of significant figures to ensure the accuracy of the result.

Best Practices for Significant Figures

To ensure the accuracy of calculations, follow these best practices:

Carry the correct number of significant figures: When performing calculations, carry the correct number of significant figures to avoid errors.
Round to the correct number of significant figures: When rounding a value, round to the correct number of significant figures to avoid errors.
Avoid excessive rounding: Avoid excessive rounding, as it can lead to errors.

Conclusion

In conclusion, the number $$8.90 \times 10^6$$ has 4 significant figures. Understanding significant figures is essential in mathematics and science, and following best practices can help ensure the accuracy of calculations.

Frequently Asked Questions

Q: What are significant figures?

A: Significant figures are the digits in a number that are known to be reliable and certain.

Q: How do I count significant figures?

A: To count significant figures, follow the rules: non-zero digits are significant, zeros between non-zero digits are significant, leading zeros are not significant, and trailing zeros are significant only if the number contains a decimal point.

Q: Why are significant figures important?

A: Significant figures are important because they help us understand the precision of a measurement or a calculated value, and they ensure the accuracy of calculations.

Q: How do I round to the correct number of significant figures?

A: To round to the correct number of significant figures, follow the rules: round up if the digit to be rounded is greater than or equal to 5, and round down if the digit to be rounded is less than 5.

References

[1] "Significant Figures." Khan Academy, Khan Academy, www.khanacademy.org/science/chemistry/x5501c7f-x5501c81/significant-figures/x5501c7f.
[2] "Significant Figures." Math Is Fun, mathisfun.com/numbers/significant-figures.html.

Introduction

Significant figures are a crucial concept in mathematics and science, and understanding them is essential for accurate calculations. In this article, we will answer some frequently asked questions about significant figures.

Q&A

Q: What are significant figures?

A: 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.

Q: How do I count significant figures?

A: To count significant figures, follow the rules:

Non-zero digits: All non-zero digits are significant.
Zeros between non-zero digits: Zeros between non-zero digits are significant.
Leading zeros: Leading zeros are not significant.
Trailing zeros: Trailing zeros are significant only if the number contains a decimal point.

Q: Why are significant figures important?

A: Significant figures are important because they help us understand the precision of a measurement or a calculated value, and they ensure the accuracy of calculations.

Q: How do I round to the correct number of significant figures?

A: To round to the correct number of significant figures, follow the rules:

Round up if the digit to be rounded is greater than or equal to 5: If the digit to be rounded is greater than or equal to 5, round up to the next significant figure.
Round down if the digit to be rounded is less than 5: If the digit to be rounded is less than 5, round down to the previous significant figure.

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, while significant figures refer to the number of digits that are known to be reliable and certain.

Q: How do I determine the number of significant figures in a calculated value?

A: To determine the number of significant figures in a calculated value, follow these steps:

Determine the number of significant figures in each value: Determine the number of significant figures in each value used in the calculation.
Round the result to the correct number of significant figures: Round the result to the correct number of significant figures based on the values used in the calculation.

Q: Can I have a fraction of a significant figure?

A: No, you cannot have a fraction of a significant figure. Significant figures are whole numbers that represent the number of digits that are known to be reliable and certain.

Q: How do I handle significant figures in scientific notation?

A: In scientific notation, the exponent is not a significant figure. Only the digits in the coefficient are significant figures.

Q: Can I use significant figures in non-scientific contexts?

A: Yes, significant figures can be used in non-scientific contexts, such as finance or engineering, where precision and accuracy are important.

Conclusion

Significant figures are a crucial concept in mathematics and science, and understanding them is essential for accurate calculations. By following the rules and guidelines outlined in this article, you can confidently apply significant figures in a variety of contexts.

References

[1] "Significant Figures." Wikipedia, Wikimedia Foundation, en.wikipedia.org/wiki/Significant_figures.
[2] "Significant Figures." Wolfram MathWorld, mathworld.wolfram.com/SignificantFigures.html.