Embark on a journey through the realm of significant figures and scientific notation, where precision and clarity intertwine. This definitive guide, the “Significant Figures and Scientific Notation Worksheet Answer Key,” unravels the intricacies of these concepts, providing a roadmap for navigating the complexities of scientific calculations.
Delve into the fundamental principles of significant figures, unraveling the rules that govern their determination and unraveling the mysteries of scientific notation, a powerful tool for representing numbers spanning vast orders of magnitude. Together, these concepts form the cornerstone of scientific communication, ensuring accuracy and consistency in the exchange of scientific knowledge.
Significant Figures and Scientific Notation: Significant Figures And Scientific Notation Worksheet Answer Key
Significant figures are the digits in a number that are known with certainty plus one uncertain digit. The rules for determining the number of significant figures in a number are as follows:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Trailing zeros after a decimal point are significant.
- Leading zeros before a non-zero digit are not significant.
For example, the number 123.45 has five significant figures, while the number 0.0012 has two significant figures.
Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more compact form. A number in scientific notation is written as a coefficient between 1 and 10 multiplied by a power of 10. For example, the number 602,214,129,000,000,000,000,000 can be written in scientific notation as 6.02214129 x 10^23.
To convert a number to scientific notation, move the decimal point until there is only one non-zero digit to the left of the decimal point. Then, count the number of places the decimal point was moved and multiply the coefficient by 10 raised to the power of the number of places the decimal point was moved.
For example, to convert 123.45 to scientific notation, move the decimal point two places to the left and multiply by 10^2, resulting in 1.2345 x 10^2.
To convert a number from scientific notation to standard notation, move the decimal point the number of places indicated by the exponent. For example, to convert 6.02214129 x 10^23 to standard notation, move the decimal point 23 places to the right, resulting in 602,214,129,000,000,000,000,000.
Significant Figures in Calculations, Significant figures and scientific notation worksheet answer key
When performing calculations with numbers that have different numbers of significant figures, the answer must be rounded to the least number of significant figures of the numbers being multiplied or divided. For example, if you multiply 12.34 (three significant figures) by 5.6 (two significant figures), the answer must be rounded to two significant figures, resulting in 69.0.
When adding or subtracting numbers with different numbers of significant figures, the answer must be rounded to the least number of decimal places of the numbers being added or subtracted. For example, if you add 12.34 (three decimal places) to 5.678 (four decimal places), the answer must be rounded to three decimal places, resulting in 18.018.
Applications of Significant Figures
Significant figures are important in scientific calculations because they allow us to express the uncertainty in our measurements. The number of significant figures in a measurement tells us how many digits are known with certainty. For example, a measurement of 12.34 cm has three significant figures, which means that the measurement is known to be between 12.335 cm and 12.345 cm.
Significant figures are also used in a variety of scientific fields, such as chemistry, physics, and biology. For example, in chemistry, significant figures are used to calculate the molar mass of a compound. In physics, significant figures are used to calculate the uncertainty in a measurement.
In biology, significant figures are used to calculate the concentration of a solution.
Worksheet Answer Key
| Problem | Answer |
|---|---|
| How many significant figures are in the number 123.45? | 5 |
| Convert the number 602,214,129,000,000,000,000,000 to scientific notation. | 6.02214129 x 10^23 |
| Multiply 12.34 by 5.6. | 69.0 |
| Add 12.34 to 5.678. | 18.018 |
| What is the uncertainty in a measurement of 12.34 cm? | ±0.005 cm |
Common Mistakes
- Counting leading zeros as significant figures.
- Not rounding the answer to the correct number of significant figures.
- Using the wrong number of decimal places when adding or subtracting numbers with different numbers of decimal places.
FAQ Explained
What is the definition of a significant figure?
A significant figure is any digit in a number that is not zero, as well as any zero that is between two non-zero digits or at the end of a number.
How do I convert a number to scientific notation?
To convert a number to scientific notation, move the decimal point until there is only one non-zero digit to the left of the decimal point. The exponent of the base 10 will be the number of places the decimal point was moved.
What are the rules for performing calculations with significant figures?
When performing calculations with significant figures, the answer must be rounded to the least number of significant figures of the numbers being added, subtracted, multiplied, or divided.
