Download Scientific Notation

8.EE.4 Operations in
Scientific Notation
EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
1) 4.9 X 102
1) 490
2) 3.75 X 10-2
2) .0375
3) 5.95 X 10-4
3) .000595
4) 9.46 X 103
4) 9460
5) 3.87 X 101
5) 38.7
6) 7.10 X 100
6) 7.10
7) 8.2 X 10-5
7) .000082
Multiplication
When multiplying numbers written in scientific
notation…..multiply the coefficients and add the
exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply (3.2 x 2.1).
Add the exponents (10-3 x 105) = 10-3 + 5
Answer: 6.7 x 102
Foldable Example
(2.6 x 105) x (3 x 102)
Foldable Example 2
(3.2 x 10-3) (4.3 x 105)
Let’s Practice…
(4 x 103) x (2 x 102)
(3.22 x 10-3) x (8 x 105)
Scientific Notation Word Problems
Apple’s iPhone 6 has a thickness of 2.7 x 10-1
inches. What would be the thickness (in inches)
of 20 iPhone 6’s stacked on top of one another?
What operation will be used to solve this
problem?
Scientific Notation Word Problems
For the 2014 season, the cast of The
Big Bang Theory each earned $1.0 x
106 per episode. If the cast filmed 15
episodes, how much total salary did
they earn? What operation will be
used to solve this problem?
Practice Problems
1)
(8x105)(7x109)
4) (2x108)(6x10-3)
1)
(2x10-5)(4x10-3)
5) (3.12 x 102)(6.501 x 105)
1)
(9x10-3)(5x104)
6) (5.1403 x 101)(7.1 x 104)
Division
Divide the coefficients. Subtract the exponent in the
denominator from the exponent in the numerator.
Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Solution: Divide 6.4 ÷ 1.7
Subtract the exponents 6 - 2
Answer: 3.8 x 104
Foldable Example
(5.4 x 106)
(1.2 x 103)
Foldable Example 2
(6 x 107)
(8 x 104)
Scientific Notation Word Problems
Tennessee covers an area of 4.2146 x 104 square miles.
The largest state, Alaska, covers 5.87878 x 105 square
miles. About how many times greater is the area covered
by Alaska than by Tennessee? What operation will be
used to solve this problem?
The area of the Pacific Ocean is 6.0 x 107 square miles. The
area of the Atlantic Ocean is 2.96 x 107 square miles. About
how many times greater is the area of the Pacific Ocean
than the Atlantic Ocean?
Practice with Quotients
•
(8 x 103)
•
3) (9.64 x 1012) / (2.5 x 107)
•
(4 x 106) ÷ (5 x 103)
•
(6 x 10-4) / (2 x 103)
(4 x 102)
•
(7 x 108)
(4 x 105)
Addition and Subtraction
To add or subtract numbers written in scientific
notation, you must….express them with the same
power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)
Solution: Since the two numbers are not expressed as the same
power of ten, one of the numbers will have to be rewritten in the
same power of ten as the other.
5.8 x 103 = .58 x 104
so (.58 x 104) + (2.16 x 104) =?
Answer: 2.74 x 104
Foldable Example 1
(4.5 x 107) + (2.5 x 107)
Foldable Example 2
(4.5 x 107) + (2.5 x 108)
Foldable Example 3
(8.7 x 105) – (4 x 105)
Foldable Example 4
(8.7 x 105) – (4 x 103)
Adding and Subtracting
1)
(6.2 x 103) + (1.3 x 103)
4) (6.2 x 103) - (1.3 x 103)
2)
(3.4 x 10-2) + (4.6 x 10-1)
5) (5.8 x 10-2) - (4.6 x 10-1)
3)
(7.2 x 108) + (2.3 x 107)
6) (7.2 x 108) - (2.3 x 107)