Algebra II LP set 21
From Brush Schools Wiki
Class: Algebra II
Lesson: Set 21 Scientific Notation
Objective: Students will write numbers in scientific notation and simplify when multiplying and dividing
Standard: 1.1 Demonstrate meanings for real numbers*, absolute value*, and scientific notation* using physical materials and technology in problem solving situations*. ES
- Procedure:
- Prior knowledge
- 5th grade introduced; developed in 7th grade math and science classes.
- 8th grade defined: n x 10^e. If e positive large number; if e negative small number where the number (n) is between 1 and 10. The number (n) can equal 1 but not 10.
- Review commutative property of multiplication. ab = ba so order does not matter when multiplying terms.
- New information
- 3 x 10^3 x 5 x 10^5
- rearrange: 2 x 5 x 10^3 x 10^5
- solve: 15 x 10^(3+5)
- 15 x 10^8
- since 15 is not between 1 and 10, we rewrite as 1.5 x 10^1
- We now have 1.5 x 10^1 x 10^8 = 1.5 x 10^(1+8)
- Final answer is 1.5 x 10^9
- So 3 x 10^3 x 5 X 10^5 is equal to 1.5 x 10^9 Mathemagical!
- Connect prior knowledge and new information
- Amazingly there is really nothing new. By combining what you know about the commutative property of multiplication and scientific notation you can now simplify problems involving multiplication and dividing of very large and very small numbers.
- Example:
- Now let's put it all together.
- Simplify: (0.0003 x 10^-6)(4000)/ (0.006 x 10^15)(2000 x 10^4)
- Step 1 -- rewrite all terms into proper scientific notation.
- (3 x 10^-4 x 10^-6 x 4 x 10^3)/(6 x 10^-3 x 10^15 x 2 x 10^3 x 10^4)
- Step 2 -- (3 x 4 x 10^-4 x 10^-6 x 10^3)/(6 x 2 x 10^-3 x 10^15 x 10^3 x 10^4)
- Step 3 -- (12 x 10^(-4-6+3))/(12 x 10^(-3+15+3+4))
- Step 4 -- (12 x 10^-7)/(12 x 10^19)
- Step 5 -- (12/12) x (10^-7 / 10^19) note: move the denominator into the numerator
- Step 6 -- 1 x (10^-7 x 10^-19) note: remember when moving from denominator to numerator, the exponent changes signs.
- Step 7 -- 1 x 10^-26
Conclusion:
In your own words, summarize the steps above.
Note: “If the teacher summarizes, it’s the teacher who gets the benefit of the closure exercise, not the student.” Jane E. Pollock Improving Student Learning One Teacher at a Time.
Student practice and more examples if needed:
From set 21, problem 14
Resources:
