Exponential Notation Overview

Overview

This lecture introduces exponential (scientific) notation, explains how calculators display it, and clarifies the meaning of positive and negative exponents.

Exponential Notation Basics

• Exponential (scientific) notation uses the form N × 10ⁿ, where N is a number from 1 to 9.999...
• N must have one nonzero digit to the left of the decimal (1-9).
• Scientific notation allows for concise representation of very large or very small numbers.

Calculator Display and E Notation

• Many calculators use "E" to represent "× 10" in scientific notation.
• For example, 12,300 is entered/displayed as 1.23 × 10⁴ or 1.23E4.
• Numbers less than one use negative exponents, e.g., 4.56 × 10⁻³ is 4.56E–3.

Understanding Exponents on the Number Line

• Positive exponents (n > 0) indicate numbers greater than one.
• Negative exponents (n < 0) represent numbers between zero and one, not negative numbers.
• Negative exponents "shrink" the value; they do not make it negative unless the original N is negative.

Key Terms & Definitions

• Exponential Notation — Writing numbers as N × 10ⁿ, where N is 1–9.999... and n is an integer.
• E Notation — Calculator format for scientific notation; "E" stands for "× 10".
• Positive Exponent — Exponent greater than zero, denotes a number greater than one.
• Negative Exponent — Exponent less than zero, denotes a number between zero and one.

Action Items / Next Steps

• Complete the three preparation problems and three follow-up questions on exponential notation.