Scientific Notation8.EE.3

Objective(s) I can write, add, and subtract numbers

in scientific notation. I can understand what is meant by the

term leading digit.

Review

Vocabulary A positive, finite decimal s is said to be written

in scientific notation if it is expressed as a product d x where d is a finite decimal so that 1 ≤ d < 10, and n is used as an integer.

The integer n is called the order of magnitude of the decimal d x .

The finite decimal is equal to every one of the following:

However, only the first is a representation of in scientific notation. Why?

Are the following numbers written in scientific notation? If not, state why.

Are the following numbers written in scientific notation? If not, state why.

Exercise 1: Exercise 2:

Exercise 3: Exercise 4:

Exercise 5: Exercise 6:

Are the following numbers written in scientific notation? If not, state why.

Are the following numbers written in scientific notation? If not, state why.

Exercise 1: Exercise 2: yes no; d < 1

Exercise 3: Exercise 4: yes no; it is being added

Exercise 5: Exercise 6: no; d > 10, and 5 yes

needs to be 10

Finding the difference Let’s say we need to determine the

difference in the populations of Texas and North Dakota.

In , Texas had a population of about million people.

North Dakota had a population of about .

Step 1: Write in Standard Form26 million = 26,000,000

6.9 x = 69,000

Step 2:Find the difference:

26,000,000- 69,00025,931,000

Step 3: Rewrite in Scientific Notation25,931,000 = 2.5931 x

On your output page…The table below shows the debt of the three most populous states and the three least populous states.

State Debt (in dollars) Population (2012)

California

New York

Texas

North Dakota

Vermont

Wyoming

Complete the ExercisesUse the table to answer the following questions:

State Debt (in dollars)Population

(2012)

California

New York

Texas

North Dakota

Vermont

Wyoming

1. What is the sum of the debts for the three most populous states? Express your answer in scientific notation.

2. What is the sum of the debt for the three least populous states? Express your answer in scientific notation.

3. How much larger is the combined debt of the three most populous states than that of the three least populous states? Express your answer in scientific notation.

In your groups…All planets revolve around the sun in elliptical orbits. Uranus’s furthest distance from the sun is approximately km, and its closest distance is approximately km. Using this information, what is the average distance of Uranus from the sun?

Answer…All planets revolve around the sun in elliptical orbits. Uranus’s furthest distance from the sun is approximately km, and its closest distance is approximately km. Using this information, what is the average distance of Uranus from the sun?

On average, Uranus is km from the sun.

Rapid Response I’m going to write a problem on the

board, you need to respond by raising your board. I will tell you either yes or no, and give you direction as to what you need to fix.

Reflect The leading digit in scientific notation

MUST be between what numbers?

Why are we interested in writing numbers in scientific notation?

Lesson QuizThe land of “Far Far Away” is about 3.671 x miles away from Earth.

The planet of “Mylantia” is about 4.444 x miles from Earth.

Find the difference in their distances from Earth. Express in Scientific Notation.

Problem Set This problem set is due tomorrow. YOU

MUST EXPLAIN YOUR THOUGHT PROCESS.