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Technical Science Scientific Tools and Methods Scientific Notation

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Scientific Notation 4 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 4 Very often scientists are forced to work with very large or very small numbers. 1 of 9 Home 4 The sun is 93 million miles from earth. –93,000,000 miles 4 Bacterial cells measure about 1 micrometer. –1 um = 0.000001 meters 4 A computer has a 10 gigabyte hard drive. –10 Gb = 10,000,000,000 bytes

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Purpose of Scientific Notation 4 There are some problems with these very large and very small numbers. 2 of 9 4 It’s easy to accidentally forget a zero or add an extra one. 4 Calculating with these numbers is also difficult. Some have too many digits to be entered on a calculator. 93,000,000 mi0.000001 m10,000,000,000 bytes

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Purpose of Scientific Notation 4 Scientific notation was developed to solve the problem of writing very large and small numbers. 3 of 9 4 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 10 7 StemPower of 10

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Purpose of Scientific Notation 4 Let’s take a closer look at the parts of a number written in scientific notation to see how it works. 4 of 9 4 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. 93,000,000 = 9.3 x 10 7 Stem

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Purpose of Scientific Notation Which number below is written in scientific notation? 5 of 9 1.82 x 10 -6 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. – 1.82 x 10 -6 – 18.2 x 10 6 – 0.182 x 10 6

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Purpose of Scientific Notation 4 The power of ten has two parts. There is a base and there is an exponent 6 of 9 4 The base will always be 10. 4 The exponent in this example is 7. 93,000,000 = 9.3 x 10 7 Base = 10 Exponent = 7

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Purpose of Scientific Notation 4 The power of ten part is a short way of writing all the zeros. 6 of 9 4 10 7 means 10 multiplied by itself 7 times. –10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 4 Here are some other examples. –10 3 = 10 x 10 x 10 = 1000 –10 2 = 10 x 10 = 100 93,000,000 = 9.3 x 10 7

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Purpose of Scientific Notation 4 Let’s put it all together and see how scientific notation works. 7 of 9 9.3 x 10 7 = 93,000,000 9.3 x 10,000,000 = 93,000,000 6.83 x 10 3 = 6,830 6.83 x 1,000 = 6,830

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Purpose of Scientific Notation 8 of 9 4 Multiplying by a multiple of ten can be done by moving the decimal. 4 The exponent on the “power of ten” tells how many places to move the decimal. 4 The “power of ten” part of a number in scientific notation is a multiple of 10. 93,000,000 = 9.3 x 10 7 10 7 = 10,000,000 9 3,000,000. 7 places 9.3 x 10 7

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Purpose of Scientific Notation Which number below is written in scientific notation? 9 of 9 8.5 x 10 4 is the only number that is written strictly in scientific notation because the base must be 10. – 1.82 x 6 10 – 8.5 x 10 4 – 3.1 x 100 6 Home

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Convert Standard Form to Scientific Notation 4 Writing a number in scientific notation is a three step process. 1 of 10 Home 4 We will start by writing large numbers in scientific notation then we will write small numbers in scientific notation. 4 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 Write 8,760,000,000 in scientific notation. 2 of 10 4 Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. 8 7 6 0 0 0 0 0 0 0.. 8.76 is the Stem

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Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. 3 of 10 4 Step 2: The number of places you moved the decimal will be the exponent on the power of 10 8 7 6 0 0 0 0 0 0 0.. 8.76 is the Stem 9 places 10 9 is the Power of 10

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Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. 4 of 10 4 Step 3: Write the number so it is the stem times the power of ten. 8 7 6 0 0 0 0 0 0 0.. 8.76 is the Stem 9 places 10 9 is the Power of 10 8.76 x 10 9 = 8,760,000,000

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Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. 5 of 10 660,000,000= 90300= 397= 4,500,000= 8,000,100,000= 159,400= 7,300= 6.6 x 10 8 9.03 x 10 4 3.97 x 10 2 4.5 x 10 6 8.0001 x 10 9 1.594 x 10 5 7.3 x 10 3

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Convert Standard Form to Scientific Notation 4 There are two differences when writing a small number in scientific notation. 6 of 10 4 First, the decimal will be moved in the opposite direction. 4 Second, the exponent will be written as a negative number.

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Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. 7 of 10 4 Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. 0 0 0 0 0 0 0 0 0 4 8 2.. 4.82 is the Stem

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Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. 8 of 10 0 0 0 0 0 0 0 0 0 4 8 2.. 4.82 is the Stem 4 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 10 -9 is the Power of 10

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Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. 9 of 10 0 0 0 0 0 0 0 0 0 4 8 2.. 4.82 is the Stem 4 Step 3: Write the number so it is the stem times the power of ten. 9 places 10 -9 is the Power of 10 4.82 x 10 -9 = 0.00000000482

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Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. 10 of 10 0.00543= 0.00000074= 0.03397= 0.00006008= 0.00000000081= 0.000105= 0.0000073= 5.43 x 10 -3 7.4 x 10 -7 3.397 x 10 -2 6.008 x 10 -5 8.1 x 10 -10 1.05 x 10 -4 7.3 x 10 -6

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Convert Scientific Notation to Standard Form 4 Converting scientific notation to a number in standard form is the same process in reverse. 1 of 5 Home 4 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 Write 1.98 x 10 9 in standard form. 2 of 5 4 The exponent tells us to move the decimal 9 places. 4 A positive exponent means the number is bigger than the stem. To make 1.98 bigger, we must move the decimal to the right. 1 9 8 x 10 9. 0 0 0 0 0 0 0. 1.98 x 10 9 = 1,980,000,000 9 places

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Write the following numbers in standard form. 3 of 5 2.9 x 10 4 = 6.87 x 10 6 = 1.008 x 10 9 = 3.04 x 10 5 = 8.8 x 10 10 = 7.52 x 10 2 = 5.73 x 10 7 = 29,000 6,870,000 1,008,000,000 304,000 88,000,000,000 752 57,300,000 Convert Scientific Notation to Standard Form

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Write 5.37 x 10 -9 in standard form. 4 of 5 4 The exponent tells us to move the decimal 9 places. 4 A negative exponent means the number is smaller than the stem. To make 5.37 smaller, we must move the decimal to the left. 5 3 7 x 10 -9. 0 0 0 0 0 0 0 0 0. 5.37 x 10 -9 = 0.00000000537 9 places

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Write the following numbers in standard form. 5 of 5 2.9 x 10 -4 = 6.87 x 10 -6 = 1.008 x 10 -9 = 3.04 x 10 -5 = 8.8 x 10 -10 = 7.52 x 10 -2 = 5.73 x 10 -7 = 0.00029 0.00000687 0.000000001008 0.0000304 0.00000000088 0.0752 0.000000573 Convert Scientific Notation to Standard Form Home

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Technical Science Scientific Tools and Methods You have completed Scientific Notation

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