6) 273000.0 = _______________________ Catalyst A pattern exists in number 1-5. Take a stab at solving #6 using the same pattern. 1) 3,450,000.0 = 3.45 x 106 2) 1,240,000,000.0 = 1.24 x 109 3) 0.000072 = 7.2 x 10-5 4) 0.00000837 = 8.37 x 10-6 5) 8370000.0 = 8.37 x 106 6) 273000.0 = _______________________

SCIENTIFIC NOTATION HW TONIGHT! Announcements SCIENTIFIC NOTATION HW TONIGHT!

Scientific Notation Practice Practice! Today’s Agenda Catalyst Scientific Notation Practice Practice!

SWBAT write numbers like a scientist. Today’s Objectives SWBAT write numbers like a scientist. SWBAT multiply, divide, and square numbers expressed in scientific notation.

Problem When scientists are talking about light wavelengths, they are usually discussing nanometers, which is 10-9 meters or 0.00000001 meters. When scientists are talking about distances in space, they are usually discussing astronomical units (AU). 1 AU is 93,000,000 miles. Fun fact: 1 AU= distance from earth to moon.

Problem SCIENTIFIC NOTATION!!!! I don’t know about you, but I ain’t about to write all them zeros. If only there was a way to fix this… SCIENTIFIC NOTATION!!!!

Notes – Scientific Notation a way of abbreviating very large or small numbers. Exponent 3.03 x 106 3 Parts! Number Power of 10

Scientific Notation Only 1 non-zero number to the left of the decimal point 3.03 x 106

How to write numbers in scientific notation Move it to the left or move it to the right Add your exponent Then it’s aaaaaalright!

Big Numbers  Scientific Notation Let’s get rid of them zeroes at the end! To do this, move the decimal point to the LEFT (to the left) 3 2 4 0 0 0 0 0 .

Small Numbers  Scientific Notation Let’s get rid of them zeroes at the front! To do this, move the decimal point to the RIGHT (to the right) 0 0 0 0 0 0 2 6 .

Small Numbers  Scientific Notation So how do we use that number 6??? 0 0 0 0 0 0 2 6 . x 10-6

Positive and Negative Exponents If the number is BIG then the exponent is POSITIVE; if the number is small then the exponent is NEGATIVE. Big = + exponent Small = - exponent

Positive Exponent 5 6 Every time you move the decimal to the RIGHT, exponent DECREASES by 1. x 103 . 2

Positive Exponent 5 6 x 10 . 1 2

Positive Exponent 5 6 x 10 . 1 Final answer: 5600

The speed of light is 300,000,000 meters per second! Scientific Notation The speed of light is 300,000,000 meters per second! How do we write this in scientific notation?

The speed of light is 300,000,000 meters per second! Scientific Notation The speed of light is 300,000,000 meters per second! How do we write this in scientific notation? 3.0 x 108

The size of a bacterium cell is 0.000055 Scientific Notation The size of a bacterium cell is 0.000055 How would you write its size in scientific notation?

Scientific Notation 00005.5 5.5 x 10-5

Now that we have the basics, let’s learn how to multiply and divide scientific notation!

Multiplying Scientific Notation Multiply the numbers ADD the exponents (7.50 x 105 ) * (6.1 x 103 ) = 46 x 108

Dividing in Scientific Notation Divide the numbers SUBTRACT the exponents (7.50 x 103 ) / (6.1 x 105 ) = 1.2 x 10-2

Squaring in Scientific Notation Square the numbers MULTIPLY the exponents (7.50 x 103 )2= 7.52 x 103x2 = 56.25 x 106 = 5.62 x 107

How Can You Do it Easily on Your Calculator? 1.) Begin by placing an open parentheses around your number 2.) To get a base at a power of 10, hit the 2nd button and then the , button. You should see an uppercase E show up on your screen. This is the equivalent to x10. 3.) After the E, type the power that the number is raised to 4.) Close the parentheses 5.) Use whichever operations (+, -, *, /, ^) that the problem requires. 6.) Repeat steps 1-4 for other number 7.) Hit enter to solve!