Snow Day Notes
01-10-25
We are transitioning into some math-heavy work that will necessarily utilize, for the rest of the semester, significant figures. The rules to significant figures are lengthy but it is essential to understand and use them. We will begin to use equations which will make use of numbers with units.
I plan to start covering 2.1: Atomic Structure sometime during Monday’s class.
Topics to Read for Friday
Please read and understand the following topics. This should take approximately 30-50 minutes. Links are provided to guide you to the appropriate reading material.
Much of the topics listed below will be review for many of you.
Scientific Notation
Scientific notation (shown right) is used to describe very large or very small numbers (left).
\[1~500~000 = 1.5\times 10^6\]
\[0.000~002~30 = 2.30 \times 10^{-6}\]
The part of the representation that contains significant figures (e.g. 1.5 or 2.30) is called the significand or mantissa. The digits in the base and exponent (106 or 10–6) are considered exact numbers.
Normalized scientific notation has its first non-zero digit in the ones place.
\[\begin{align*} 34.5\times 10^3 ~~~~&\mathrm{not ~normalized} \\[1.5ex] 3.45\times 10^4 ~~~~&\mathrm{normalized} \end{align*}\]
Metric prefixes
Metric prefxies are a unit prefix that precedes a basic unit of measure.
Units (SI and others)
Units are dimensions that are attached to any measured number (ft for length, s for time, etc.). Familiarize yourself with the SI Base Units as well as Imperial vs. Metric units.
Accuracy vs. Precision
Know the difference between accuracy and precision.
Experimental and Percent Error
Know how to calculate experimental and percent error.
Significant Figures
Know and understand the rules to significant figures. This includes:
- How to count the number of significant figures in a number
- How to determine the number of significant figures in a final answer to a calculation. There are specific rules to consider when adding/subtracting or multiplying/dividing numbers.
- How to deal with significant figures when adding/subtracting numbers written in scientific notation
- How to deal with significant figures when taking the log or antilog of a number
- How to round a final answer to the correct number of significant figures
Dimensional Analysis
Know how to convert between dimensions (i.e. dimensional analysis) using the factor-label method. I will use this method for calculations throughout the semester.
Basic equations
- Temperature conversions between K, °C, and °F.
- Density