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Scientific Notation Writing large and small numbers

WARM UP 1.Simplify : 2. 3k – 5 = 7k Express the area of the triangle as a single exponential expression: 2q 6q³

SCIENTIFIC NOTATION OBJECTIVE You will learn: First, how to express numbers in scientific notation and standard form Then, how to find the products and quotients of numbers expressed in scientific notation

It’s easy to make mistakes when computing with small numbers such as and large numbers such as 75,000,000. People who deal regularly with such numbers use scientific notation. Scientific notation – a method of writing very large and very small numbers using powers of 10. Take for example, an ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across

Written in scientific notation: Number of atoms in a penny; 2.0 x Size of each atom: 3.0 x The sign on the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

Writing Scientific Notation Scientific notation is written using the product of 2 factors. 1.0 x 10 6 = 1,000,000 First factor is a number ≥ 1 but < 10. 1,000,000 = 1.0 Second factor is a power of 10 = (10 6 )

Scientific Notation to Standard Notation Write each number in standard notation x x 10,000, = 10,000,000 26,400,000 Think: Move the decimal right 7 places for positive exponent x x 1/10, = 1/10, Think: Move the decimal left 4 places for negative exponent.

Standard Notation to Scientific Notation Write each number in scientific notation Move the decimal to get a number between 1 and 10 2 x 10 □ Set up scientific notation. Think: decimal needs to move left 6 places to change 2 to , moving left makes exponent negative. 2 x Move the decimal to get a number between 1 and x 10 □ Set up scientific notation. Think: decimal needs to move left 3 places to change 2.7 to , moving left makes exponent negative. 2.7 x 10 -3

Math Fact !!!!! The mass (weight) of the earth is about 5,980,000,000,000,000,000,000,000 kilograms. (5 septillion, 980 sextillion) This is written in scientific notation as 5.98 x How would you enter this into your calculator?

Ever wonder what 1 million pennies looks like? Here’s your answer.

Videos Scientific Notation me-G4rc6NIhttp:// me-G4rc6NI Multiplication/Division of Scientific Notation FOlirz4Jshttps:// FOlirz4Js

Flipped Classroom Lesson on Scientific Notation kV46CXjq4

HOMEWORKHOMEWORK Chapter 1 Lesson 6

Scientific Notation with a Calculator Technology Lab with TI-83 calculator

Scientist often have to work with very large or very small numbers. For example, the Andromeda Galaxy contains over 200,000,000,000 (billion) stars. Scientific notation is a compact way of expressing these numbers. Show 200,000,000,000 in scientific notation on your graphing calculator. Enter 200,000,000,000 on your calculator. Press [ENTER]

2 E 11 on the graphing calculator display means 2 x Your calculator automatically puts very large numbers into scientific notation.

You can enter scientific notation directly into the calculator yourself using the EE function key (2 nd key then comma, key). Enter 2 x by pressing 2 [2 nd ] EE [,] 11 [enter]

Evaluating Expressions using Scientific Notation Evaluate 230,000,000 x 650,000 First write 230,000,000 in scientific notation = 2.3 x 10 8 Second write 650,000 in scientific notation = 6.5 x 10 5 Press 2.3 [2 nd ] EE [,] 8 x 6.5 [2 nd ] EE [,] 5 [enter] In scientific notation, 230,000,000 x 650,000 is equal to x or 149,500,000,000,000 (149 trillion, 500 billion).

Evaluate (340,000,000,000 ÷ 1,235) x 4,568 Write each number in scientific notation. 340,000,000,000 = 3.4 x ,235 = x ,568 = x 10 3 Press (3.4 [2 nd ] EE [,] 11 ÷ [2 nd ] EE [,] 3 ) x [2 nd ] EE [,] 3 [enter] (340,000,000,000 ÷ 1,235) x 4,568 = x (because this calculator displays results to only 10 decimal places, this in not exact. The exact answer is x )

Problem Solving In space, light travels about 9,460,000,000,000 kilometers per year. This distance is known as a light- year. The star Altair is 16.3 light-years from earth. Write this distance in scientific notation. Suppose the universe is made up of 125,000,000,000 galaxies, each containing 200,000,000,000 stars. Use this data to find the total number of stars in the entire universe. Express your answer in scientific notation and in standard form.

Answer (check out what these would look like in standard notation) 1.54 E 14 kilometers from earth 2.5 E 22 star in the universe

154,000,000,000, trillion kilometers 25,000,000,000,000,000,000, sextillion stars in the universe

Extremely small numbers are written in the same way but use (-) negative exponents. For example, our ordinary penny contains about 20 sextillion atoms, written: 2.0E22 or 20,000,000,000,000,000,000 atoms The average size of the atom we discussed earlier is about 3 hundred millionths centimeters across, written: 3.0E-8 or centimeters

Helpful Hint The sign of the exponent tells which direction to move the decimal. A positive exponent means to move the decimal to the right. A negative exponent means move the decimal to the left.