Scientific Notation Notes CCSS Math 8.EE.A.3 ©IDEA GALAXY Scientific Notation Notes CCSS Math 8.EE.A.3 7 x 108 700,000,000

©IDEA GALAXY Scientific Notation

How many stars are in the Milky Way Galaxy? https://commons.wikimedia.org/wiki/File:Milky_Way_Galaxy.jpg 100,000,000,000 stars

What is the diameter of a grain of sand? 0.0024 inch https://commons.wikimedia.org/wiki/File:Sand_from_Gobi_Desert.jpg

What is the world population? https://www.flickr.com/photos/gsfc/8246931247 7,000,000,000

How long is a red blood cell? https://www.flickr.com/photos/53921113@N02/5645665364 0.000008 meters long

So many zeroes! 100,000,000,000 0.0024 7,000,000,000 0.000008 Scientists and mathematicians realized that working with really large numbers and really small numbers could get messy. To solve this problem, they developed a shorthand to write very large and very small numbers without so many place values.

Lesson Objective I can convert numbers from standard form to scientific notation and from scientific notation to standard form.

Keys to Remember 1) Scientific Notation is a way to represent really big numbers and really small numbers. 2) Numbers larger than one have positive exponents in scientific notation. 3) Numbers between zero and one have negative exponents in scientific notation.

Big numbers Big numbers are represented with x 10 to a positive power. When you multiply a number by 10 to a positive power the number gets bigger by powers of 10. 5 x 103 = 5000 7 x 108 = 700,000,000 2.25 x 107 = 22,500,000

Small numbers Small numbers are represented with x 10 to a negative power. When you multiply a number by 10 to a negative power the number gets smaller by powers of 10. 5 x 10-2 = .05 5 x 10-5 = 0.00005 3.78 x 10-7 = 0.000000378

Is it a really big number or a really small number? huge number 5 694,500 6.945 X 10 small number -7 0.0000009019 9.019 X 10 -6 small number 0.000002568 2.568 X 10 huge number 2,568,000 6 2.568 X 10

Is it a really big number or a really small number? tiny number -5 0.0000309 3.09 X 10 small number -6 0.00000101 1.01 X 10 6 huge number 2,568,000 2.568 X 10 huge number 3,400,000,000 9 3.4 X 10

Questions to ask when converting from standard form to scientific notation… Is this a big number or a small number? Will the exponent be positive or negative? Where’s the decimal point? How many places will the decimal move until the ones place is directly on its left? How do we rewrite the number in scientific notation?

What is 42,356 in scientific notation? Is this a big number or a small number? Will the exponent be positive or negative? Where’s the decimal point? How many places will the decimal move until the ones place is directly on its left? How do we rewrite the number in scientific notation? 4 4.2356 x 10

What is .0967 in scientific notation? Is this a big number or a small number? Will the exponent be positive or negative? Where’s the decimal point? How many places will it move until there is nothing past the ones place? How do we rewrite the number in scientific notation? -2 9.67 x 10

Let’s Try Some… 1) How do you write the following number in scientific notation: 546,789 5.46789 X 10 5

Let’s Try Some… 2) How do you write the following number in scientific notation: 0.0000345 3.45 x 10 -5

Let’s Try Some… 3) How do you write the following number in scientific notation: 0.567543 5.67543 x 10 -1

Let’s Try Some… 4) How do you write the following number in scientific notation: 123,456,789 1.23456789 x 10 8

Questions to ask when converting from scientific notations to standard form… Is this a big number or a small number? Which way will you move the decimal point? How many places will the decimal point move? How do we rewrite the number in standard notation?

Scientific Notation to Standard Form 4 5.045 x 10 Is this a big number or a small number? Which way will you move the decimal point? How many places will the decimal point move? How do we rewrite the number in standard notation? 50,450

Scientific Notation to Standard Form -5 2.33 x 10 Is this a big number or a small number? Which way will you move the decimal point? How many places will the decimal point move? How do we rewrite the number in standard notation? 0.0000233

Let’s Try Some… 5) How do you write the following number in standard form: 3.45 x 10 3,450,000 6

Let’s Try Some… 6) How do you write the following number in standard form: 4.056 x 10 405,600,000 8

Let’s Try Some… 7) How do you write the following number in standard form: 4.056 x 10 .00000004056 -8

Let’s Try Some… 8) How do you write the following number in standard form: 5.212 x 10 .00005212 -5