Technical Science Scientific Tools and Methods

1. Technical ScienceScientific Tools and Methods Scientific Notation

2. 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.

3. 1 of 9 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

4. 2 of 9 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.

5. 3 of 9 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

6. 4 of 9 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.

7. 5 of 9 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.

8. 6 of 9 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.

9. 6 of 9 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

10. 7 of 9 Purpose of Scientific Notation • Let’s put it all together and see how scientific notation works. 9.3 x 107 = 93,000,000 10,000,000 x 93,000,000 = 9.3 6.83 x 103 = 6,830 = 1,000 x 6,830 6.83

11. 8 of 9 Purpose of Scientific Notation • The “power of ten” part of a number in scientific notation is a multiple of 10. 107 = 10,000,000 9 3,000,000. 93,000,000 = 9.3 x 107 9.3 x 10 7 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.

12. 9 of 9 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.

13. 1 of 10 Convert Standard Formto 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.

14. 2 of 10 Convert Standard Formto 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

15. 3 of 10 Convert Standard Formto 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

16. 4 of 10 Convert Standard Formto 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

17. 5 of 10 Convert Standard Formto 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

18. 6 of 10 Convert Standard Formto 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.

19. 7 of 10 Convert Standard Formto 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

20. 8 of 10 Convert Standard Formto 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

21. 9 of 10 Convert Standard Formto 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 10 -9 is the Power of 10 4.82 is the Stem 4.82 x 10 -9 = 0.00000000482

22. 10 of 10 Convert Standard Formto 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

23. 1 of 5 Convert Scientific Notationto 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

24. 2 of 5 Convert Scientific Notationto 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. . . 0 0 0 0 0 0 0 1 9 8 x 10 9 9 places 1.98 x 109 = 1,980,000,000

25. 3 of 5 Convert Scientific Notationto Standard Form • 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

26. 4 of 5 Convert Scientific Notationto 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

27. 5 of 5 Convert Scientific Notationto Standard Form 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

28. Technical ScienceScientific Tools and Methods You have completed Scientific Notation