Significant figures and dimensional analysis worksheet answers provide a crucial foundation for understanding and solving problems in science and engineering. This guide delves into the concepts of significant figures, dimensional analysis, and provides comprehensive answers to worksheet problems, empowering learners to master these essential skills.
By understanding the rules for determining significant figures and applying dimensional analysis techniques, individuals can ensure the accuracy and precision of their calculations, leading to more reliable and meaningful results.
Significant Figures and Dimensional Analysis Worksheet Answers
Significant Figures, Significant figures and dimensional analysis worksheet answers
Significant figures are the digits in a number that are known with certainty plus one uncertain digit. The rules for determining significant figures are as follows:
- All non-zero digits are significant.
- Zeroes between non-zero digits are significant.
- Zeroes at the end of a number are significant only if there is a decimal point.
- Zeroes at the beginning of a number are not significant.
For example, the number 123 has three significant figures, the number 100 has two significant figures, and the number 0.001 has one significant figure.
Dimensional Analysis
Dimensional analysis is a technique that can be used to check the validity of equations and to solve problems. The basic principle of dimensional analysis is that the units of the answer must be the same as the units of the question.
To use dimensional analysis, first write down the equation that you are trying to solve. Then, identify the units of each term in the equation. If the units of the answer are not the same as the units of the question, then the equation is not valid.
Dimensional analysis can also be used to solve problems. To solve a problem using dimensional analysis, first write down the problem in equation form. Then, identify the units of each term in the equation. Finally, use the units to solve for the unknown variable.
For example, suppose you want to find the volume of a cube with a side length of 3 cm. The equation for the volume of a cube is V = s³, where V is the volume and s is the side length.
The units of the volume are cm³, and the units of the side length are cm. Therefore, the answer must be in cm³.
To solve the problem, we can substitute the given value of the side length into the equation: V = (3 cm)³ = 27 cm³.
Worksheet Answers
The following worksheet contains practice problems on significant figures and dimensional analysis. The answers to the problems are provided at the end of the worksheet.
| Problem | Answer |
|---|---|
| How many significant figures are in the number 123.45? | 5 |
| How many significant figures are in the number 0.0012? | 2 |
| Convert 25 inches to centimeters. (1 inch = 2.54 cm) | 63.5 cm |
| The density of water is 1 g/cm³. What is the mass of 500 cm³ of water? | 500 g |
Popular Questions
What are significant figures?
Significant figures are the digits in a number that are known with certainty, plus one estimated digit.
How do I determine the number of significant figures in a number?
Follow the rules for determining significant figures, which include considering zeros, leading zeros, and trailing zeros.
What is dimensional analysis?
Dimensional analysis is a technique used to check the validity of equations and to convert units between different systems.
How do I use dimensional analysis to solve problems?
Set up the problem using the given quantities, convert units as needed, and solve for the unknown quantity.
