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Scientific Notation

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WARM UP

1) 0.035 ÷ 0.05 = 0.7

2) Solve 0.6 ÷ 0.05 = 12

3) 0.00132 ÷ 0.012 = 0.11

4) Without changing the quotient, change the problem so that the divisor is a whole number

68. 13 ÷ 0.003

It will be 68,130 ÷ 3

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Lets review what we learned in the earlier lesson

To divide any two decimal numbers first move the decimal point in the divisor to the right so that it becomes a whole number

Move the decimal point of the dividend the same number of places to the right as you did of the divisor

Now divide as you do with whole numbers

Put the decimal point for your answer directly abovethe one in your dividend

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Let us take an example

9.09 ÷ 4.5

4.5 ) 9 .09 0 9 0 9 0 9 0 0

2.02 In the case of a remainder add zero to the dividend and divide until there is no remainder or until there are 4 decimal places in the answer

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Today we are going to learn about Scientific Notation

Scientific Notation is a way to express very large or very small numbers.

It is most often used in “scientific” calculations where the analysis must be very precise

Scientific notation has two parts

• A non zero number between 1 and 10

• A power of 10

Lets get started

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A number in scientific notation is written as the product of a number between 1 and 10 (integer or decimal ) and an integer power of 10

A number written in scientific notation has the form

N X 10r

where, N is between 1 and 10 r is an integer

What is Scientific notation ?

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To Change from Standard form to Scientific notation

Place the decimal point so that there is one non zero digit to the left of the decimal point

Count the number of decimal places the decimal point has “ moved ” from the original number. This will be the exponent (power) of 10

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Lets take some Examples

10,000 = 1 x 104

65,000,000 = 6.5 x 107

The power of ten indicates how many places the decimal point has moved from the original number

Standard form to Scientific notation

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100 = 1

101= 10

102 = 10 X 10 =100

10000 = 100 x 100 = 1.0000 x 104

If the decimal point is moved N places to the leftThe power of ten is increased by N units

POSITIVE EXPONENTS

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NEGATIVE EXPONENTS

1 X 10-1 = 1 = 0.1 (one tenth) 10

1 X 10-2 = 1 = 0.01 (0ne hundredth) 100 If the decimal place is moved N places to the right

then the power of 10 is decreased by N units

.01 = .01 x 100 = 1 x 10-2

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If the original number is less than 1, then the exponent is negative .

If the original number is greater than 1, then the exponent is positive

579,300,000 = 5.793 x 108 (Positive exponent)

0.000246 = 2.46 x 10-4 (Negative exponents)

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To change Scientific notation to Standard form

Move the decimal point to the right for positive exponent 10

Move the decimal point to the left for negative exponent10

Use zeros to fill in places

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Lets take some examples

3.367 x 106 = 3,367,000

The decimal point has moved 6 places to the right

8.951 x 10-4 = 0.0008951

The decimal point has moved 4 places to the left

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You try some !

1)72,500 = 7.25 x 105

2) 27,100,000 = 2.71 x 107

3)5.56 x 109 = 5.56 billion

4)1.976 x 10-4 = 0.0001976

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BREAK TIME

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Lets play a Game

Click on the photo to color a picture

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One light year is the distance light travels in one year. If the speed of light is 3 x 105 kilometers per second, about how many kilometers does light travel in one year ?

About 9.51 x 1012 km

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According to the Aluminum Association, 2,031,000,000 pounds of aluminum cans were recycled in 1993. At an average of 29.9 cans per pound, how many aluminum cans were recycled that year ? Express your answer in scientific notation.

5.95 x 1010 cans

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Scientists divide Earth’s history in to small units based on the types of life-forms living on then. In the Jurassic period, which occurred about 208,000,000 years ago, dinosaurs ruled. Express the years in scientific notation.

2.08 x 108

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Assessment

1. Write each number in scientific notation:a) 34,000 3.4 x 104

b) 165,000,000,000 1.65 x 1011

c) 310,210 3.10 x 105

2. Write each number in standard form:a) 3.05 x 102 305

b) 2 x 1011 200,000,000,000

c) 9.037 x 108 903,700,000

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Assessment

3. The distance from our sun to the nearest star, Alpha Centauri, is about 42,000,000,000,000 kilometers. Write this distance in scientific notation.

4.2 x 1013

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Lets review what we have learned in this lesson

Scientific notation can be expressed as the short way to write very large or very small numbers without writing all the zeros

A number in scientific notation is written as the product of a number that is between 1 and 10 and an integer that is power of ten

The power of ten is written with an exponent (negative or positive )

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To change from standard form to Scientific notation

Place the decimal point so that there is a non zero digit to the left of the decimal point

Count the number of decimal places the decimal point has “moved” from the original number

If the original number was less than 1, then the exponent is negative. If the original number is greater than 1,then the exponent is positive

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Lets take a few examples

93,000,000 = 9.3 x 107

(Standard form to Scientific notation)

7.8 x 106 = 7,80,0000

( Scientific notation to standard form)

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You had a Great Lesson Today

Be sure to practice what you have learned today