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**Technical Science Scientific Tools and Methods**

Scientific Notation

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**Scientific Notation In this section you will …**

Describe the purpose of Scientific Notation Convert numbers in standard form to scientific notation Convert numbers in scientific notation to standard form.

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**Purpose of Scientific Notation**

Home Very often scientists are forced to work with very large or very small numbers. The sun is 93 million miles from earth. 93,000,000 miles Bacterial cells measure about 1 micrometer. 1 um = meters A computer has a 10 gigabyte hard drive. 10 Gb = 10,000,000,000 bytes

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**Purpose of Scientific Notation**

There are some problems with these very large and very small numbers. 93,000,000 mi m 10,000,000,000 bytes It’s easy to accidentally forget a zero or add an extra one. Calculating with these numbers is also difficult. Some have too many digits to be entered on a calculator.

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**Purpose of Scientific Notation**

Scientific notation was developed to solve the problem of writing very large and small numbers. Numbers written in scientific notation have two parts: a stem, which is a number between 1 & 10, and a power of 10. 93,000,000 = 9.3 x 107 Stem Power of 10

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**Purpose of Scientific Notation**

Let’s take a closer look at the parts of a number written in scientific notation to see how it works. 93,000,000 = 9.3 x 107 Stem The stem is always a number between 1 and 10. In this example, 9.3 is the stem and it is between 1 and 10.

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**Purpose of Scientific Notation**

Which number below is written in scientific notation? 1.82 x 10-6 18.2 x 106 0.182 x 106 1.82 x is the only number that is written strictly in scientific notation because it is the only one with a stem that is between 1 and 10.

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**Purpose of Scientific Notation**

The power of ten has two parts. There is a base and there is an exponent Exponent = 7 93,000,000 = 9.3 x 107 Base = 10 The base will always be 10. The exponent in this example is 7.

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**Purpose of Scientific Notation**

The power of ten part is a short way of writing all the zeros. 93,000,000 = 9.3 x 107 107 means 10 multiplied by itself 7 times. 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 Here are some other examples. 103 = 10 x 10 x 10 = 1000 102 = 10 x 10 = 100

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**Purpose of Scientific Notation**

Let’s put it all together and see how scientific notation works. x = 93,000,000 9.3 x 10,000,000 = 93,000,000 x = 6,830 6.83 x 1,000 = 6,830

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**Purpose of Scientific Notation**

The “power of ten” part of a number in scientific notation is a multiple of 10. 107 = 10,000,000 93,000,000 = 9.3 x 107 9.3 x 10 7 9 3,000,000. 7 places Multiplying by a multiple of ten can be done by moving the decimal. The exponent on the “power of ten” tells how many places to move the decimal.

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**Purpose of Scientific Notation**

Home Which number below is written in scientific notation? 1.82 x 610 8.5 x 104 3.1 x 1006 8.5 x 10 4 is the only number that is written strictly in scientific notation because the base must be 10.

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**Convert Standard Form to Scientific Notation**

1 of 10 Convert Standard Form to Scientific Notation Home Writing a number in scientific notation is a three step process. We will start by writing large numbers in scientific notation then we will write small numbers in scientific notation. You will see a step by step example and then you will have a chance to practice.

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**Convert Standard Form to Scientific Notation**

2 of 10 Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . . 8.76 is the Stem

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**Convert Standard Form to Scientific Notation**

3 of 10 Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. Step 2: The number of places you moved the decimal will be the exponent on the power of 10 . . 9 places 8.76 is the Stem 10 9 is the Power of 10

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**Convert Standard Form to Scientific Notation**

4 of 10 Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. Step 3: Write the number so it is the stem times the power of ten. . . 9 places 8.76 is the Stem 10 9 is the Power of 10 8.76 x = 8,760,000,000

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**Convert Standard Form to Scientific Notation**

5 of 10 Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. 660,000,000 = = 397 = 4,500,000 = 8,000,100,000 = 159,400 = 7,300 = 6.6 x 108 9.03 x 104 3.97 x 102 4.5 x 106 x 109 x 105 7.3 x 103

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**Convert Standard Form to Scientific Notation**

6 of 10 Convert Standard Form to Scientific Notation There are two differences when writing a small number in scientific notation. First, the decimal will be moved in the opposite direction. Second, the exponent will be written as a negative number.

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**Convert Standard Form to Scientific Notation**

7 of 10 Convert Standard Form to Scientific Notation Write in scientific notation. Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . . 4.82 is the Stem

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**Convert Standard Form to Scientific Notation**

8 of 10 Convert Standard Form to Scientific Notation Write in scientific notation. Step 2: The number of places you moved the decimal will be the exponent on the power of 10. The exponent will be negative because you started with a number less than 1. . . 9 places 4.82 is the Stem 10 -9 is the Power of 10

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**Convert Standard Form to Scientific Notation**

9 of 10 Convert Standard Form to Scientific Notation Write in scientific notation. Step 3: Write the number so it is the stem times the power of ten. . . 9 places 4.82 is the Stem 10 -9 is the Power of 10 4.82 x =

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**Convert Standard Form to Scientific Notation**

10 of 10 Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. = = = = = = = 5.43 x 7.4 x x x 8.1 x 1.05 x 7.3 x

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**Convert Scientific Notation to Standard Form**

1 of 5 Convert Scientific Notation to Standard Form Home Converting scientific notation to a number in standard form is the same process in reverse. The exponent tells you how many places to move the decimal on the stem. A positive exponent says the number is bigger than the stem; move the decimal accordingly A negative exponent says the number is smaller than the stem; move the decimal accordingly

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**Convert Scientific Notation to Standard Form**

2 of 5 Convert Scientific Notation to Standard Form Write x 109 in standard form. The exponent tells us to move the decimal 9 places. A positive exponent means the number is bigger than the stem. To make 1.98 bigger, we must move the decimal to the right. . x 10 9 . 9 places 1.98 x 109 = 1,980,000,000

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**Convert Scientific Notation to Standard Form**

3 of 5 Write the following numbers in standard form. 2.9 x 104 = 6.87 x 106 = 1.008 x 109 = 3.04 x 105 = 8.8 x = 7.52 x 102 = 5.73 x 107 = 29,000 6,870,000 1,008,000,000 304,000 88,000,000,000 752 57,300,000

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**Convert Scientific Notation to Standard Form**

4 of 5 Convert Scientific Notation to Standard Form Write x in standard form. The exponent tells us to move the decimal 9 places. A negative exponent means the number is smaller than the stem. To make 5.37 smaller, we must move the decimal to the left. . x . 9 places 5.37 x =

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**Convert Scientific Notation to Standard Form**

5 of 5 Home Write the following numbers in standard form. 2.9 x = 6.87 x = 1.008 x = 3.04 x = 8.8 x = 7.52 x = 5.73 x = 0.0752

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**Technical Science Scientific Tools and Methods**

You have completed Scientific Notation

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