Transcript scientific notation
DO NOW
• Pass out calculators. • Warm Up Questions: 1. What is the solution to the system of equations shown below? Y = 2x – 2 8x + 2y = - 16 2. What value of n makes this equation true? 7 + 3(6 – 4n) = 2n A. -0.56 B. 0.4
C. 2.5
D. 12.5
Objective:
To numbers in scientific notation and to compare two numbers written in scientific notation .
How many turkey ’s were raised in the U.S. IN 2005??
256,000,000
How much does the earth way???
6,588,000,00000 0,000,000,000,0 00,000,000 TONS
How many atoms does a quarter contain??
97, 700, 000, 000,000,000,00 0,000,000,000 … atoms.
What is the average size of an atom?
The average size of an atom is about 0.00000003 centimeters across.
• Numbers written in scientific notation are written as two factors. One factor is a number greater than or equal to 1 and less than 10. The other factor is a power of 10.
Writing Math
To write scientific notation for numbers greater than or equal to 1 and less than 10, use a 0 exponent. 5.63 = 5.63 x 10 ° .
EXAMPLE 1 Write numbers in standard form a.
2.0075 10 6 = 2,007,500
Exponent is
6
.
Move decimal point
6
places to the right.
b.
1.685 10 -4 = 0.0001685
Exponent is
–
4
.
Move decimal point
4
places to the left.
Write the number in standard notation.
1.35
10 5
1.35 1.35 10 5 100,000 135,000
* Move the decimal from where you want it to where it actually is.
Helpful Hint
A positive exponent means move the decimal to the right, and a negative the decimal to the left.
exponent means move
Write the number in standard notation.
1.9
10 –5
1.9 1.9 10 –5 1 100,000 1.9 100,000 0.000019
10 = 1 100,000 Divide by the reciprocal.
Think: Move the decimal left 5 places.
EXAMPLE 2 Write numbers in scientific notation a.
42,590,000 = 4.259 10 7
Move decimal point 7 the left.
places to Exponent is 7 .
b.
0.0000574 = 5.74 10 -5
Move decimal point
5
places to the right.
Exponent is
–
5
.
Example 2A: Translating Standard Notation to Scientific Notation Write 250790 in scientific notation.
Check It Out: Example 2B Write 0.000811 in scientific notation.
0.000811
8.11
Think: The decimal needs to move 4 places to get a number between 1 and 10.
8.11 10
Set up scientific notation.
Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative.
So 0.000811 written in scientific notation is 8.11 Check 8.11 10 –4 .
0.0001 = 0.000811
GUIDED PRACTICE for Examples 1 and 2 Write the number
539,000
in scientific notation. Then write the number
4.5
10 – 4
in standard form.
1.
539,000 = 5.39 10 5 4.5 10 – 4 = 0.00045
EXAMPLE 4 Compute with numbers in scientific notation Evaluate the expression. Write your answer in scientific notation.
a.
(8.5 10 2 )(1.7 10 6 )
=
(8.5 • 1.7) (10 2 • 10 6 )
=
14.45
10 8
Commutative property and associative property Product of powers property =
(1.445 10 1 ) 10 8
=
1.445 (10 1
=
1.445 10 9 )
Write 14.45
in scientific notation.
Associative property Product of powers property
EXAMPLE 4 Compute with numbers in scientific notation b.
(1.5 10 3 ) 2
=
1.5
2 (10 3 ) 2
=
2.25
(10 6 )
Power of a product property Power of a power property c.
1.2 10 4 1.6
10 −3
= =
1.2
1.6
0.75
10 4 10 – 3 (10 7 ) 10 7
=
(7.5 10 1 )
=
7.5 (10 – 1
=
7.5
(10 6 ) 10 7 )
Product rule for fractions Quotient of powers property Write 0.75
in scientific notation.
Associative property Product of powers property
GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression. Write your answer in scientific notation.
3.
(1.3 10 5 ) 2
=
1.69
(10 – 10 )
4.
4.5 10 5 – 1.5
10 2
=
3 10 7
5.
(1.1 10 7 ) (4.2 10 2 )
=
4.62
10 9
Scientific Notation:
A brand new one-dollar bill is 4.3x10
-3 inches thick. What would be the thickness of a stack of 200 brand new one-dollar bills?
Scientific Notation:
One mole of an element is defined as a sample containing 6.0 x 10 23 atoms of that element. Based on the information, how many atoms are there in 1.5 x 10 -4 mole of an element?
Scientific Notation:
On February 2, 2013, the U.S. Treasury estimated the national debt at $1.2278 x 10 13 . The U.S. Census Bureau ’s estimate for that population was about 3.086 x 10 8 . Using these estimates calculate the per person share of the national debt.
Scientific Notation:
A red blood cell is 8 x 10 -6 meters long. A skin cell is 3 x 10 -5 meters long. How many times longer is the skin blood cell than the red blood cell.
Scientific Notation:
The start Vega is approximately 2.38 x 10 14 kilometers from earth. The start Antares is approximately 4.94 x 10 15 kilometers from earth. How much further from earth is the start Antares than the star Vega?
Scientific Notation:
A ship ’s weight is 1.2 x 10 4 tons when it is empty. The ship ’s cargo, fuel, and crew weigh a total of 4.6 x 10 3 tons. What is the total weight of the ship with the cargo, fuel, and crew onboard?