Name Date PD SCIENTIFIC NOTATION

Name Date PD SCIENTIFIC NOTATION

Name: Scientific Notation Date: Class: Definition: A number in scientific notation is written as a product of two factors in the form of a 10 n, where n is an integer and 1 a 10. What does that mean in words? What is the purpose of using scientific notation? Recognizing Scientific Notation Is each number written in scientific notation? If not, give a reason why it is not. 1. 0.6 10 2..2 2 10. 1 10..2 10. 2 010 1

Understanding Powers of 10 (Numbers 10 or more): Standard Form Product of Factors Scientific Notation 0 00 000 9600 Summary: The coefficient is than 1 and than 10. For numbers greater than or equal to 10, use a exponent. Understanding Powers of 10 (Numbers Less Than 1): Standard Form Product of Factors Scientific Notation 0.2 2

0.0 0.00 Summary: The coefficient is than 1 and than 10. For numbers less than 1, use a exponent. Writing a Number in Scientific Notation: 1.,000,000 2. 0.000000002. 200. 0.0009 Try It! Write each number in scientific notation. a) 2. b) 6.2 c) 0.000 d) 0.006

Writing a Number in Standard Form: 1.. 10 2..2 10. 2.1 10..2 2 10 Summary of Scientific Notation: Positive exponents make the decimal move to the. Negative exponents make the decimal move to the. Try It! Write each number in standard form. a) 9 10 b) 2. 2 10 c). 10 d).1 10 Practice Is each number written in scientific notation? If not, give a reason why it is not. 1. A horse-chestnut has a diameter of about 0 2 10 cm. 2. The approximate wavelength of infrared light is 0.01 10 meter.. Neptune is about 9. 10 km from the sun.

. A football field (excluding end zones) is 1 10 10 yards long. Writing a Number in Scientific Notation:. 6,000 6. 0.00006. 00.0002. 9,60,000 Writing a Number in Standard Form: 9. 6. 10 10. 9.2 10 11..2 10. 10

Multiplying/Dividing Perform the following operations; leave your answer in scientific notation. Example 1: ( 10 )() Example 2: (9)(2 10 ) Try-It! 6 a) (2 10 )() b) ( 10 )(6) Example : ( 10 )(10 ) Example : ( 10 10 )( ) Try-It! a) (6 10 )(210 ) b) (10 )( 10 ) 6

Example : (1. 10 2 )(10 ) Try-It: (9.10 )(210 ) Example 6: In 2010, the population in the United States will be about.09 10. Spending for health care will be about $ per person. About how much will the US spend on health care in 2010? Try-It: The average American household spends about $1,6 each year. If there are about 1.2 10 households, what is the approximate amount of money spent by American households in one year?

Perform the following operations; leave your answer in scientific notation. Example : 9 10 Try-It!: 6 10 2 9 Example : 610 210 9 Try-It!: 910 10 Example 9:.9 10 10 Try-It!:.2 10 610 Example 10: 1.6 10 9 210 Try-It!: 2.10 11 2 10 Example 11:.6 10 210 Try-It!: 1.2 10 10 11 9 Example : There are about 9 billion devices ( 9 10 ) connected to the Internet. If a wireless router can support 00 devices, how many wireless routers are necessary to connect all 9 billion devices wirelessly? Practice: Perform the following operations; leave your answer in scientific notation. 6 1) (2 10 )(10 ) 6 2) )(10 ( 10 )

1 ) ( 10 )(.110 ) 16 ) (9.2 10 )(10 ) 2. 10 ) 9 10 6.10 6) 10 9.610 ) 2 10 610 10 210 ) 9) The distance light travels in one year (one light year) is about. 10 miles. The closest star to Earth (other than the Sun) is Alpha Centauri, which is. light years from Earth. About how many miles from Earth is Alpha Centauri? 22 10) A conservative estimate of the number of stars in the universe is 6 10. The average human can see about,000 stars at night with his naked eye. About how many times more stars are there in the universe, compared to the stars a human can actually see? 9

Practice Perform the following operations; leave your answer in scientific notation. 2 6 1. 2 10 10 2. 2 10 10. 1 10. 10. 2.110 10..210 2 10 6. 10 10 6. 10 10. 10 9 10 10 9. Light travels 1.110 inches in 1 second. About how far will light travel in 1 minute? Use scientific notation. Simplify the following: 6 10. x x 11. y 9 y 10

Perform the following operations; leave your answer in scientific notation. 1 610.. 10 1. 2 10. 10 1. 210.6 10 1. 2 10 1.10 16. 9 1.2 10 1 1.10 1. 1 9 10 Simplify the following: 6 r 1. 2 r k 19. 2 2 k 20. A box contains 1. x 10 2 atoms. One third of them are carbon, the other two thirds are oxygen. How many carbon atoms are in the box? Use scientific notation. 11

Adding and Subtracting Perform the following operations; leave your answer in scientific notation. Example 1: ( 10 ) (610 ) Example 2: (2.9 10 ) (9.6110 ) Try-It! a) (210 ) (610 ) 6 6 b) (.0 10 ) (1.010 ) Example : (9 10 ) (10 ) Example : (9.61 10 ) (2.9 10 ) Try-It! a) (.10 ) (2.10 ) b) ( 10 ) (10 )

Example : ( 10 ) (210 ) Example 6: 1 ( 10 ) (9.6 10 ) Try-It! a) (6 10 ) ( 10 ) 1 1 b) (2.1 10 ) (.10 ) Example : ( 10 ) (10 ) Example : 1 (9.6 10 ) (10 ) Try-It! a) (9.2 10 ) ( 10 ) 20 1 b) (6. 10 ) (.2 10 ) Example 9: ( 10 ) (10 1 ) Example 10: (10 10 ) (210 9 ) Example 11: (610 10 1 ) (2 ) 1

Example : A flight from Singapore to New York includes a stopover in Hawaii. The distance between Singapore and Hawaii is about 6. 10 miles. The distance between New York and Hawaii is about.9 10 miles. a) Find the total distance from Singapore to New York. b) How much farther is the first half of the trip compared to the second half of the trip? Try-It!: At a given time, Saturn was 9.1 10 miles from the Sun and Earth was 9. 10 miles from the Sun. By what distance is one planet closer to the Sun than the other planet? Practice Perform the following operations; leave your answer in scientific notation. 1. (9 10 ) (610 ) 2. (6. 10 ) (2. 10 ). ( 10 ) (10 ). (1.2 10 ) (.6 10 ). (6 10 ) ( 10 ) 1 6. (. 10 ) (. 10 ) 1

. (. 10 ) (.110 ) 1. (9.6 10 ) (9.6 10 ) 9. (610 ) ( 10 ) 10. (.10 ) (.110 ) 11: Salt water on Earth has an approximate surface area of.2 10 km 2 and fresh water on Earth has an 6 approximate surface area of 9 10 km 2. How much of Earth s surface is covered by water, including both salt and fresh water? Write your answer in scientific notation. 1

Warm-Up: About how many times larger is Venus than Mars? Round answers to the nearest tenth. About how many times larger is Earth than Mars? Round answers to the nearest tenth. Planets Volume (km ) When comparing 2 numbers in scientific notation: Venus 9. 10 11 Compare the powers of 10 to determine which number is greater. If the powers are equal compare coefficients. Earth 1.1 10 Mars 11 1.6 10 Identify the greater number in each pair of numbers. Justify your reasoning. Example 1: 2.6 10 2.1 10 Example 2:. 10 1 1.1 10 1 Try It! Identify the lesser number. a).2 2 1 10 6. 10 b).6 10. 10 16

Comparing a number in Standard Form to a number in Scientific Notation: Example : Which number is larger?,00,000.9 10 Example : There are.16 10 spectators in a stadium watching a football game. In a theater there are 1,10 people watching a concert. Which venue has more people? Show your work. Try It! a) Which is the larger number? 6.9 10 0. 00 b) An actor has,6 followers on Facebook. A musician has has less fans? Show your work.. 10 followers on Twitter. Who 1

Practice In the answer blanks below write:,, or. 1..2 2 10 2.110 2.. 10 10. 6. 1 10 9. 10..6 10. 10 16 910. 10 )(10 ) 10 10 ( 6..610 11 210. ( 10 ) ( 10 ). 10. 1,000,000 ( 10 ) (210 ) 9. 6 6,0,000.9 10 10. 9.6 10, 00 2 11. In 2000 Americans consumed an average of.2 lbs of potatoes, and.96 10 lbs of dairy products per person. Did Americans consume more potatoes or dairy products? Show your work.. The average diameter of a type of round shaped bacteria is 0.00000 meters. The spacing between two of these bacteria is 2.1 9 10 meters. Which length is smaller? Show your work. 1