Catalyst – January (62-(2*5), 2010 Describe the pattern you see in the first 5. After, fill in the 6th

answer.

1) 3,450,000.= 3.45 x 106

2) 1,240,000,000.= 1.24 x 109

3) 0.000072 = 7.2 x 10-5

4) 0.00000837 = 8.37 x 10-6

5) 8370000.= 8.37 x 106

6) 273000. = _________________________

Today’s Agenda

Catalyst Scientific Notation Practice Intro to Dimensional Analysis Practice! Exit Question

Today’s Objectives

SWBAT write numbers like a scientist/G.

SWBAT convert units like a scientist/G.

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.

Problem

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

Key Point #1 : Scientific notation is a way of abbreviating very large or very small numbers.

3.03 x 106

3 Parts!

Number Power of 10

Exponent

Scientific Notation

Key Point #2: A number in correct scientific notation has only one non-zero number to the left of the decimal.

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 NotationLet’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

.

Big Numbers Scientific Notation

How many times do we move the decimal to the LEFT (to the left)?

3 2 4 0 0 0 0 0

.

Big Numbers Scientific Notation…the decimal moves SEVEN times

to the LEFT.

3.2 4 0 0 0 0 0

Big Numbers Scientific Notation

So, how do we use that number 7???

3.2 4

0 0 0 0 0x 107

Big Numbers Scientific Notation

How many times do we move the decimal 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

How many times did we move the decimal to the RIGHT (to the right)?

0 0 0 0 0 0 2 6.

Small Numbers Scientific Notation

…the decimal moves SIX times 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 Key Point #3:

If the number is BIG then

the exponent is POSITIVE; if the number is small then the exponent is NEGATIVE.

Positive Exponent

5 6x 1032.

Every time you move the decimal to the RIGHT, exponent DECREASES by 1.

Positive Exponent

5 6 x 102. 10

Positive Exponent

5 6 x 1010. 0 0

Final answer: 5600

Negative Exponent

3 8. -10x 10

Final answer: 0.38

Every time you move the decimal to the LEFT, exponent INCREASES by 1.

Scientific Notation

2250000

Scientific Notation

2.250000

2.25 x 106

Scientific Notation

10 300 000 000

Scientific Notation

1.0300000000

1.03 x 1010

Scientific Notation

.000055

Scientific Notation

00005.5

5.5 x 10-5

Scientific Notation

Think of a number-line:

-10 -5 0 510

Adding/taking 0’s on right is +Adding/taking 0’s on left is -

Scientific Notation

9870000

.00000987

Scientific Notation

9870000 9.87 x 106

.00000987 9.87 x 10-6

Scientific Notation

8.1 x 103

9.4 x 10-2

Scientific Notation

8.1 x 103 8100

9.4 x 10-2 .094

CONVERSIONS

GET READY FOR AWESOME!

Convert it like it’s hot

Key Point #1: A conversion factor shows the same value

with two different units.

YOU ALREADY KNOW THIS STUFF!

Examples: 10 dimes= 1 dollar 20 nickels= 1 dollar 4 quarters= 1 dollar

Dimensional Analysis

Key Point #2: Dimensional analysis is a tool used to convert from one unit to another.

Working on the Railroad

Step 1: What to what?

Step 2: Write conversion factor(s)

Step 3: Train tracks

Practice! One-step problems. How many meters are in 10 centimeters?

How many centimeters are in 327 meters?

Practice! On your own!

The distance from New Orleans to Denver is 2258 kilometers. Convert this to meters!

Always remember…

Key Point #3: In two step problems, always convert to the unit without a prefix first.

Mass: grams Distance: meters Volume: liters Temperature: degrees Celsius

Practice…

Chris Paul has a mass of 79.4 kg, convert this to mg.

*Bonus: If a standard basketball has a mass of 620, 000 mg, how many basketballs would equal the mass of Chris Paul?

Practice

There are 1135 decaliters (daL) in a pool. Convert to liters (cL).

10 L = 1 daL

Practice!

The average human eye blink is 300 milliseconds. Convert this to hectoseconds.

Exit Question

In July 2008, it was estimated that the world’s population is about 6,707,000,000. The United States’ population was estimated to be 304,060,000. The coldest temperature ever created by man is .000000005°K. Write these 3 numbers in scientific notation.