Unit 1 Math Review AP Physics - Scientific Notation & Significant Figures

Sep 30, 2026

Uploaded by Kurz

Unit 1 AP Physics math review focuses on significant digits and scientific notation as essential tools for handling very large and very small numbers. The material explains how to represent numbers using scientific notation, emphasizing calculator entry with the EE key to store values as single numbers and avoid common input mistakes. It also defines significant figures, distinguishes exact vs. measured values, applies Atlantic/Pacific counting rules, and outlines rounding precision for addition and subtraction.

LanguageEnglish

CategoryExam

FormatPDF

Pages32

Reading Time1 h 21 min

AccessFree to download

Unit 1 Math Review AP Physics

Topics in the packet

Scientific Notation

Measurements and Significant Figures

Atlantic & Pacific Rule

Rounding in arithmetic operations

Unit 1 Math Review AP Physics Wednesday, The following topics in your packet will not be covered in class – you may check my website for notes and an answer key. You can also find more information in your textbook. 1. Significant digits (not a huge deal like in chemistry) Appendix B 2. Scientific notation – Appendix A Scientific Notation • Writing very large (much greater than 1) and very small (much less than 1) numbers is cumbersome and does not make clear how many significant figures are involved. MAKE SURE YOU PAY CLOSE ATTENTION TO THIS… • Using scientific notation with your calculator Scientific calculators all have some kind of scientific notation button . The purpose of this button is to enter numbers directly into scientific notation and make sure the calculator stores them as a single number instead of a math equation . (This prevents you from making PEMDAS errors when working with numbers in scientific notation on your calculator.) In this class we will ALWAYS USE THE EE button on your calculator – pressing EE replaces inputing x 10. Notice that when you enter EE on your calculator (depedning on the model) your calculator may only show one E – this is completely fine. DO NOT ENTER X 10 on your calculator EVER IN THIS CLASS – hopefully I made this clear =) Example: 3.82 x 10-16 x 3.0 x 10 8 You enter 3.82 EE-16 x 3.0 EE 8 ENTER The calculator answer should read 1.14E-7 You write 1.14 x10 -7 (the E is replaced with x 10 ) Measurements and Significant Figures • When we measure any quantity we can do so with only a certain precision. • We state our knowledge of a measurement through the use of significant figures: digits that are reliably known. Significant Figures • Exact numbers have no uncertainty or error ex: the 100 used to calculate percentage ex: the 2 in the equation c = 2π r • Measured numbers have some degree of uncertainty or error. • When calculations are done with measured numbers, the error of measurement is propagated, or carried along. • The number of significant figures (or digits) in a quantity is the number of reliably known digits it contains. • There are some basic rules that can be used to determine the number of significant digits in a measurement. Significant Figures • Definition: All the valid digits in a measurement, the number of which indicates the measurement’s precision (degree of exactness) . • also called significant figures, or sig figs • Use the Atlantic & Pacific Rule to determine the sig figs. PACIFIC OCEAN ATLANTIC OCEAN • Decimal is Absent – Count from the Atlantic side from the first non-zero digit. • Decimal is Present – Count all digits from the Pacific side from the first non-zero digit. Significant Figures Examples: 421 Decimal is absent-> Atlantic; three significant figures 421 000 Decimal is absent-> Atlantic; three significant figures 42.100 Decimal is present-> Pacific; five sig figs 4.201 four sig figs 0.421 three sig figs 0.000421 three sig figs To eliminate doubt, write the number in scientific notation. 4.2100 x 105 – five sig figs 4.21 x 105 – three sig figs A bar placed above a zero is also acceptable. 4, 210, 000 – five sig figs 4, 210, 000 – seven sig figs To avoid confusion, for the purpose of this course we will consider numbers with trailing zeros to be significant. ex: 20 s has two sig figs, even if it is not written as 2.0 x 101 s • When you perform any arithmetic operation, it is important to remember that the result never can be more precise than the least-precise measurement. • The final result of an addition or subtraction should have the same number of decimal places asthe quantity with the least number of decimal places used in the calculation. Example: 23.1 4.77 125.39 + 3.581 156.841 Round to 156.8 (one decimal place)

FAQs

What is scientific notation and why is it used in this course?

Scientific notation makes it easier to write very large and very small numbers while keeping track of significant figures. It is also used to prevent confusion during calculations.

How should you enter scientific notation on a calculator for this class?

Always use the EE button. Pressing EE replaces “x 10,” and you should never enter “x 10” directly in this course.

How do you determine the number of significant figures using the Atlantic & Pacific rule?

If the decimal is absent, count from the Atlantic side starting at the first non-zero digit. If the decimal is present, count all digits from the Pacific side starting at the first non-zero digit.

Sep 30, 2026

Uploaded by Kurz