Do Now 10.15.13

Is there a rule?

2 x 2 x 2 x 5 x 5

3 x 3 x 3 x 7 x 7 x 7

2 x 2 x 2 x 2 x 2 x 2 2 x 2 x 2 1

Today’s Objective Students will be

able to express a very large number or very small number in both scientific notation and standard form.

Scientific Notation• What does the sun weigh?

• 4,400,000,000,000,000,000,000,000,000,000 lbs.

• How much hydrogen does the sun burn each second?

• 600,000,000 metric tons

Scientific Notation• How much longer will the sun burn?

• 6,000,000,000 years.

Scientific Notation• Let’s look at these large Numbers• 4,400,000,000,000,000,000,000,000,000,000

lbs.

• 600,000,000 metric tons• 6,000,000,000 years• Each of these numbers can be written in a different form called Scientific Notation

Scientific Notation• Scientific Notation is made up of 2 parts.

• 1st Part = a number greater than or equal to 1, but less than 10

• 2nd Part = x 10 to some power

• If it doesn’t have both parts, it is NOT Scientific Notation.

Scientific Notation• Let’s change these large

Numbers to Scientific Notation…..

• 4,400,000,000,000,000,000,000,000,000,000 lbs.

• 4.4 x 1030 lbs.• Place the decimal pt. after the first # and then count to the end.

Change to Scientific Notation

•832,000,000•Place the decimal just after the first number.

•Then count the # of places•832,000,000 =8.32 x 108

Change to Scientific Notation

• 2450 = 2.45 x 103 • 765,000,000 = 7.65 x 108

• 0.000722 = 7.22 x 10-4 Notice that if the decimal moves right the exponent is negative and if it moves left, the decimal is positive.

Change to Scientific Notation

•0.000722•Place the decimal just after the first number.

•Then count the # of places.•000722= 7.22 x 10-4

Change to Standard Notation

•Now let’s go backwards and change from Scientific Notation to Standard Notation.

Change to Standard Notation

•4.53 x 105

•Move the decimal pt. 5 places to the right.

•453000 = 453,000

Scientific Notation•(5 x 103)(4 x 105)•5 x 4 = 20•103 x 105 = 108 •20 x 108 Now convert to

Scientific Notation

2.0 x 109

Try this one•820,000,000

Place the point after the 1st #

Count to the end8.2 x 108

8.2

Try this one•(6 x 102)(3 x 107)•6 x 3 = 18•102 x 107 = 109 •18 x 109 Now convert to

Scientific Notation

1.8 x 1010

Try this one•(5 x 103)2 = •(5 x 103) (5 x 103)•5 x 5 = 25•103 x 103 = 106 •25 x 106 = 2.5 x 107

The Distance From the Sun to the Earth

93,000,000

Step 1

• Move decimal left• Leave only one number in front of decimal

Step 2

• Write number without zeros

Step 3

• Count how many places you moved decimal• Make that your power of ten

The power often is 7 becausethe decimalmoved 7 places.

• 93,000,000 --- Standard Form

• 9.3 x 107 --- Scientific Notation

Practice Problems

1) 98,500,000 = 9.85 x 10?

2) 64,100,000,000 = 6.41 x 10?

3) 279,000,000 = 2.79 x 10?

4) 4,200,000 = 4.2 x 10?

Write in scientific notation. Decide the power of ten.

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 106

More Practice Problems

1) 734,000,000 = ______ x 108

2) 870,000,000,000 = ______x 1011

3) 90,000,000,000 = _____ x 1010

On these, decide where the decimal will be moved.

1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010

Complete Practice Problems

1) 50,0002) 7,200,0003) 802,000,000,000

Write in scientific notation.

1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Form

Move the decimal to the right

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Write in Standard Form

• 6.27 x 106

• 9.01 x 104

• 6,270,000• 90,100