Technical Science Scientific Tools and Methods Scientific Notation

Technical Science Scientific Tools and Methods Scientific Notation

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.

Purpose of Scientific Notation 1 of 9 Home 4 Very often scientists are forced to work with very large or very small numbers. 4 The sun is 93 million miles from earth. – 93, 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 bytes

Purpose of Scientific Notation 2 of 9 4 There are some problems with these very large and very small numbers. 93, 000 mi 0. 000001 m 10, 000, 000 bytes 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.

3 of 9 Purpose of Scientific Notation 4 Scientific notation was developed to solve the problem of writing very large and small numbers. 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 = 9. 3 x 107 Stem Power of 10

Purpose of Scientific Notation 4 of 9 4 Let’s take a closer look at the parts of a number written in scientific notation to see how it works. 93, 000 = 9. 3 x 107 Stem 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.

Purpose of Scientific Notation 5 of 9 ? Which number below is written in scientific notation? – 1. 82 x 10 -6 – 18. 2 x 106 – 0. 182 x 106 A 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.

6 of 9 Purpose of Scientific Notation 4 The power of ten has two parts. There is a base and there is an exponent Exponent = 7 93, 000 = 9. 3 x 107 Base = 10 4 The base will always be 10. 4 The exponent in this example is 7.

Purpose of Scientific Notation 6 of 9 4 The power of ten part is a short way of writing all the zeros. 93, 000 = 9. 3 x 107 4 107 means 10 multiplied by itself 7 times. – 10 x 10 x 10 = 10, 000 4 Here are some other examples. – 103 = 10 x 10 = 1000 – 102 = 10 x 10 = 100

7 of 9 Purpose of Scientific Notation 4 Let’s put it all together and see how scientific notation works. 9. 3 x 107 = 93, 000 9. 3 x 10, 000 = 93, 000 6. 83 x 103 6. 83 x 1, 000 = 6, 830

8 of 9 Purpose of Scientific Notation 4 The “power of ten” part of a number in scientific notation is a multiple of 10. 107 = 10, 000 9 3, 000. 93, 000 x 107 9. 3 x 10 7 = 9. 3 7 places 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.

Purpose of Scientific Notation 9 of 9 Home ? Which number below is written in scientific notation? – 1. 82 x 610 – 8. 5 x 104 – 3. 1 x 1006 A 8. 5 x 10 4 is the only number that is written strictly in scientific notation because the base must be 10.

Convert Standard Form to Scientific Notation 1 of 10 Home 4 Writing a number in scientific notation is a three step process. 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.

Convert Standard Form to Scientific Notation 2 of 10 ? Write 8, 760, 000 in scientific notation. 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. 8. 76 is the Stem

Convert Standard Form to Scientific Notation 3 of 10 ? Write 8, 760, 000 in scientific notation. 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. 9 places 8. 76 is the Stem 10 9 is the Power of 10

Convert Standard Form to Scientific Notation 4 of 10 ? Write 8, 760, 000 in scientific notation. 4 Step 3: Write the number so it is the stem times the power of ten. 8. 7 6 0 0 0 0. 9 places 8. 76 is the Stem 10 9 is the Power of 10 8. 76 x 10 9 = 8, 760, 000

Convert Standard Form to Scientific Notation 5 of 10 ? Write the following numbers in scientific notation. 660, 000 90300 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 8. 0001 x 109 1. 594 x 105 7. 3 x 103

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

Convert Standard Form to Scientific Notation 7 of 10 ? Write 0. 0000482 in scientific notation. 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 4. 8 2 4. 82 is the Stem

Convert Standard Form to Scientific Notation 8 of 10 ? Write 0. 0000482 in scientific notation. 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. 0. 0 0 0 0 4. 8 2 9 places 4. 82 is the Stem 10 -9 is the Power of 10

Convert Standard Form to Scientific Notation 9 of 10 ? Write 0. 0000482 in scientific notation. 4 Step 3: Write the number so it is the stem times the power of ten. 0. 0 0 0 0 4. 8 2 9 places 4. 82 is the Stem 10 -9 is the Power of 10 4. 82 x 10 -9 = 0. 0000482

Convert Standard Form to Scientific Notation 10 of 10 ? Write the following numbers in scientific notation. 0. 00543 0. 00000074 0. 03397 0. 00006008 0. 0000081 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

Convert Scientific Notation to Standard Form 1 of 5 Home 4 Converting scientific notation to a number in standard form is the same process in reverse. 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

Convert Scientific Notation to Standard Form 2 of 5 ? Write 1. 98 x 109 in standard form. 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. 0 09 0 0 0. 1. 9 8 0 x 010 9 places 1. 98 x 109 = 1, 980, 000

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 1010 7. 52 x 102 5. 73 x 107 = = = = 29, 000 6, 870, 000 1, 008, 000 304, 000 88, 000, 000 752 57, 300, 000

Convert Scientific Notation to Standard Form 4 of 5 ? Write 5. 37 x 10 -9 in standard form. 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. 0. 0 0 0 0 5. 3 7 x 10 -9 9 places 5. 37 x 10 -9 = 0. 0000537

Convert Scientific Notation to Standard Form 5 of 5 Home ? Write the following numbers in standard form. 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. 00001008 0. 0000304 0. 0000088 0. 0752 0. 000000573

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