# 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.

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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. 0.4C. 2.5D. 12.5 DO NOW

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.

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°. Writing Math

EXAMPLE 1 Write numbers in standard form a. 2.0075 10 6 Exponent is 6. Move decimal point 6 places to the right. b. 1.685 10 -4 Exponent is – 4. Move decimal point 4 places to the left. = 2,007,500 =0.0001685

135,000 1.35  100,000 * Move the decimal from where you want it to where it actually is. 1.35  10 5 1.35  10 5 10 = 100,000 5 Write the number in standard notation. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint

1.9  100,000 0.000019 Divide by the reciprocal. Think: Move the decimal left 5 places. 1.9  10 –5 1.9  10 –5 –5 1 10 = 100,000 Write the number in standard notation. 1.9  1 100,000

EXAMPLE 2 Write numbers in scientific notation 4.259 10 7 a. 42,590,000 = b.0.0000574=5.74 10 -5 Move decimal point 7 places to the left. Exponent is 7. 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 Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. 8.11 8.11  10 Set up scientific notation. Check 8.11  10 = 8.11  0.0001 = 0.000811 –4 Write 0.000811 in scientific notation. So 0.000811 written in scientific notation is 8.11  10 –4.

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

Compute with numbers in scientific notation EXAMPLE 4 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 = (1.445 10 1 ) = 10 8 1.445 (10 1 ) = 10 8 Commutative property and associative property Product of powers property Write 14.45 in scientific notation. Associative property 1.445 10 9 = Product of powers property

Compute with numbers in scientific notation EXAMPLE 4 b. (1.5 10 3 ) – 2 (10 3 ) – 2 = 1.5 2 (10 6 ) – = 2.25 Power of a product property Power of a power property 10 −3 c. 1.2 10 4 1.6 = 10 3 – 1.2 1.6 10 4 Product rule for fractions (10 7 ) = 0.75 (7.5 10 1 ) – = 10 7 7.5 (10 1 – = 10 7 ) (10 6 ) = 7.5 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 (10 10 ) – = 1.69 10 2 4. 4.5 10 5 – 1.5 10 7 = 3 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?

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