Technical Science Scientific Tools and Methods Scientific Notation

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.

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 = 0.000001 meters A computer has a 10 gigabyte hard drive. 10 Gb = 10,000,000,000 bytes

Purpose of Scientific Notation There are some problems with these very large and very small numbers. 93,000,000 mi 0.000001 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.

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

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.

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 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.

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.

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

Purpose of Scientific Notation Let’s put it all together and see how scientific notation works. 9.3 x 107 = 93,000,000 9.3 x 10,000,000 = 93,000,000 6.83 x 103 = 6,830 6.83 x 1,000 = 6,830

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.

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.

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.

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 7 6 0 0 0 0 0 0 0 8.76 is the Stem

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 . 8 7 6 0 0 0 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 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. . . 8 7 6 0 0 0 0 0 0 0 9 places 8.76 is the Stem 10 9 is the Power of 10 8.76 x 10 9 = 8,760,000,000

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 = 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 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.

Convert Standard Form to Scientific Notation 7 of 10 Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. 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

Convert Standard Form to Scientific Notation 8 of 10 Convert Standard Form to Scientific Notation Write 0.00000000482 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. 0 0 0 0 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 Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. Step 3: Write the number so it is the stem times the power of ten. . . 0 0 0 0 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 = 0.00000000482

Convert Standard Form to Scientific Notation 10 of 10 Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. 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

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

Convert Scientific Notation to Standard Form 2 of 5 Convert Scientific Notation to Standard Form Write 1.98 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. . 1 9 8 x 10 9 . 0 0 0 0 0 0 0 9 places 1.98 x 109 = 1,980,000,000

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 1,008,000,000 304,000 88,000,000,000 752 57,300,000

Convert Scientific Notation to Standard Form 4 of 5 Convert Scientific Notation to Standard Form Write 5.37 x 10-9 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. 0 0 0 0 0 0 0 0 0 . 5 3 7 x 10 -9 . 9 places 5.37 x 10-9 = 0.00000000537

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 0.000000001008 0.0000304 0.00000000088 0.0752 0.000000573

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