Lesson 8: Scientific Notation

What does it mean when the exponent is negative in scientific notation? positive?

How do you go from scientific notation back to a larger number?

8.EE.4: Perform operations with numbers expressed in scientific notation, including adding and subtracting numbers with the same power of 10; multiplying and dividing numbers with and without scientific notation; and expressing the answer in scientific notation.

Lesson Description
This lesson focuses on the mechanics of converting between decimal notation and scientific notation, as well as performing arithmetic operations within the notation itself. Key topics include:

The Standard Form: Understanding the requirement that a number in scientific notation must be written as a×10
n
, where 1=|a|<10 and n is an integer.

Conversion Techniques: Mastering the movement of the decimal point—shifting it left for large numbers (positive exponents) and right for small decimals (negative exponents).

Arithmetic Operations: Using the Product Rule and Quotient Rule for exponents to multiply and divide numbers in scientific notation without converting them back to "long-form" decimals first.

Significant Figures & Accuracy: Learning how to adjust the final coefficient if a calculation results in a number outside the 1=|a|<10 range (e.g., converting 45×10^3 to 4.5×10^4.

Purpose
The purpose of Section 13.8 is to equip students with the computational tools of the modern workplace. Whether a student is entering the Middlesex CC Radiologic Technology program (dealing with microscopic wavelengths) or the Environmental Science program (dealing with large-scale data), the ability to handle extreme values is essential. This section bridges the gap between abstract algebra and the actual data entry and calculation methods used in calculators and scientific software.

Depth of Knowledge (DOK) Level
DOK Level 2

Level 2 (Skill/Concept): This section requires students to apply multiple rules in a specific sequence. For example, multiplying two numbers in scientific notation requires multiplying the coefficients and then applying the Product Rule to the powers of ten. The student must then evaluate if the final answer is in the correct format and perform an additional "shift" if necessary. This involves more than just recall; it requires the flexible application of exponent properties to a specialized numerical format.

Provide some real world applications to explain the use of scientific notation and why its important to know how to convert from one to the other.

"you try" on page 316 and supplemental worksheets