The following lesson is

one lecture in a series of

Chemistry Programs

developed by

Professor Larry ByrdDepartment of Chemistry

Western Kentucky University

Excellent Assistance has been provided by:

Ms. Elizabeth RomeroMs. Kathy Barnes

Ms. Padmaja PakalaMs Sathya Sanipina

CHECK TEST #1 ANSWERS

Scientific Notation (Part 5)

1. Give the following in scientific notation. Also, write each in correctly written

computer form!A. 648 = ?

Step #1: 648

Step #2: 648.

Step #3: 648. Step #4: 6.48 x 10+2

Step #5: 6.48 x 102

Step #6: Computer form =

* Notice, that we “never” place a positive sign for the exponent in

the computer form

Always in step #1 on your paper rewrite the given problem just as it was given!

1. Give the following in scientific notation. Also, write each in correctly written

computer form!

B. 0.00162 = ?

Step #1: 0.00162

Step #2: 0.00162

Step #3: 1.62 x 10-3

Step #4: Computer Form =

Always in step #1 on your paper rewrite the given problem just as it was given!

1. Give the following in scientific notation. Also, write each in correctly written

computer form!

C. 96,000,000 (as two significant figures)

Step #1: 96,000,000 Given

Problem

Step #2: 96,000,000.

Step #3: 9.6 x 10+7

Step #4: 9.6 x 107

Step #5: Computer Form =

1. Give the following in scientific notation. Also, write each in correctly written Scientific Notation computer form!

D. 30,000,000,000 x 10-4 (as one significant figure)

Step #1: 30,000,000,000 x 10-4

Step #2: 30,000,000,000. x 10-4

Step #3: 3 x 10+10 x 10-4

Step #4: 3 x 10(+10) + (-4)

Step #5: 3 x 10+6

Step #6: 3 x 106

Step #7: Computer Form:

1. Give the following in scientific notation. Also, write each in correctly written Scientific Notation computer form!

E. 0.00468 x 10-3 (as three significant

figures)

Step #1: 0.00468 x 10-3

Step #2: 0.00468 x 10-3

Step #3: 4.68 x 10-3 x 10-3

Step #4: 4.68 x 10(-3) + (-3)

Step #5: 4.68 x 10-6

Step #6: Computer Form = 4.68E-6

1. Give the following in scientific notation. Also,write each in correctly written Scientific Notation computer form!

F. 94.6 x 10-4 (as three significant figures)

Step #1: 94.6 x 10-4 Given Problem

Step #2: 94.6 x 10-4

Step #3: 9.46 x 10+1 x 10-4

Step #4: 9.46 x 10(+1) + (-4)

Step #5: 9.46 x 10-3

Step #6: Computer Form = 9.46E-3

2. Convert the following into conventional numbers (every-day-way-of-writing-numbers). If part of the number is in scientific notation form, then you must get all the given problem into correctly written scientific notation form before converting it back into its conventional number.

A. 7.82 x 10-4

Step #1: 7.82 x 10-4

Step #2: 00007.82 x 10-4

Step #3: 0.000782

B. 9.34 x 103

Step #1: 9.34 x 103

Step #2: 9.340 x 10+3

Step #3: 9340

2. Convert the following into conventional numbers (every-day-way-of-writing-numbers). If part of the number is in scientific notation form, then you must get all the given problem into correctly written scientific notation form before converting it back into its conventional number.

C. 0.00381 x 10-2

Step #1: 0.00381 x 10-2

Step #2: 0.00381 x 10-2

Step #3: 3.81 x 10-3 x 10-2

Step #4: 3.81 x 10(-3) + (-2)

2. Convert the following into conventional numbers (every-day-way-of-writing-numbers). If part of the number is in scientific notation form, then you must get all the given problem into correctly written scientific notation form before converting it back into its conventional number.

2. Convert the following into conventional number (every-day-way-of-writing-numbers). If part of the number is in scientific notation form, then you must get all the given problem into correctly written scientific notation form before converting it back into its conventional number.

Step #5: 3.81 x 10-5

Now you convert 3.81 x 10-5 back into its convention number form

Step #6: 000003.81 x 10-5

Step #7: 0.0000381

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

You cannot do any steps-in-your-head !You must show every step you use on your sheet of paper!

A. (6.20 x 10-2) (3.00 x 10-1) = ? [Answer as 3 significant figures]

Step #1: (6.20 x 10-2) (3.00 x 10-1) Given problem

Step #2: (6.20) (3.00) x 10-2 x 10-1 Collect Similar

Terms

Step #3: 18.600 x 10(-2) + (-1) Next, Round-off

Step #4: 18.6 x 10-3

Important Note: If one part of the problem is given as a fraction then all parts must be converted into fraction forms and then treat it as a large fraction.

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

You cannot do any steps-in-your-head !You must show every step you use on your sheet of paper!

Step #5: 1.86 x 10+1 x 10-3

Step #6: 1.86 x 10(+1) + (-3)

Step #7: 1.86 x 10-2

Step#8:ComputerForm=1.86E-2

Important Note: If one part of the problem is given as a fraction then all parts must be converted into fraction forms and then treat it as a large fraction.

B. (0.514 x 10-3)(4.20 x 103) (answer as 3 significant figures)

Step #1: [ 0.514 x 10-3 ] [ 4.20 x 103 ] Given Problem

Step #2: [ 0.514 x 10-3 ] [ 4.20 x 10+3 ]

You must get each part first into Scientific Notation

Step #3: ( 5.14 x 10-1 x 10-3 ) ( 4.20 x 10+3 )

Step #4: ( 5.14 x 10(-1)+(-3) ) ( 4.20 x 10+3 )

Step #5: ( 5.14 x 10-4 ) ( 4.20 x 10+3 )

Step #6: ( 5.14 ) ( 4.20 ) x 10-4 x 10+3 Collect similar terms

Step #7: 21.588 x 10(-4) + (+3) Round-off and add exponents algebraically

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

You cannot do any steps-in-your-head !You must show every step you use on your sheet of paper!

Step #8: 21.6 x 10-1

Step #9: 2.16 x 10+1 x 10-1

Step #10: 2.16 x 10(+1)+(-1)

Step #11: 2.16 x 100

Step #12: 2.16

Step #13: Computer form = 2.16

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

You cannot do any steps-in-your-head !You must show every step you use on your sheet of paper!

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

C. (124,000) (48.1) (12.0) (1.00) (Answer as 3 significant figures)

Step #1: (124,000) (48.1) (12.0) (1.00) Given Problem

Step #2: (1.24 x 10+5) (4.81 x 10+1) (1.20 x 10+1) (1.00)

Step #3: (1.24) (4.81) (1.20) (1.00) x 10+5 x 10+1 x 10+1

Multiply first parts and then add the exponents algebraically.

Step #4: 7.15728 x 10(+5) + (+1) + (+1)

Next, Round-off !

Step #5: 7.16 x 10+7

Step #6: 7.16 x 107

Step #7: Computer Form = 7.16E7

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

You cannot do any steps-in-your-head !You must show every step you use on your sheet of paper!

Step #1:

684

2.0 6.87

Given Problem

Step #2:

684

2.0

1

6.87

Convert each part into a fraction

D.

684

2.0 6.87

= ? [Answer as 2 significant figures]

3. Use scientific notation to work the following problems: "Do" all work in scientific notation! Give "ALL" answers in scientific notation!

You cannot do any steps-in-your-head !You must show every step you use on your sheet of paper!

Step #3:

684 1

2.0 87.6

Convert into one large fraction

Step #4:

210 x 6.84 1

2.0 110 x 8.76

Step #5:

210 x 84.6

110 x 2.0 76.8

Collect similar terms

Convert all to scientific notation forms

Step #6: 210 x 84.6

110 x 7.5201

First Round-off the Numerator Part

Step #7: 210 x 84.6

110 x 8.1

Next, convert 18. into 110 x .81

Step #8: 210 x 84.6

110 x 110 x .81

Step #9: 210 x 84.6

1 1

10 x .81

Add exponents algebraically

Step #10: 210 x 84.6

210 x .81

Step #11: 210

210 x

84.6

8.1

Collect Similar Terms

Step #12:

2 2

10 x 0.2631578 Round-off and then Subtract exponents algebraically

Step #13:

2- 2

10 x 0.27 Add exponents algebraically

Step #14: 010 x 0.27

Step #15: 0.27

Step #16: 1-10x 2.7 Step #17: Computer Form = 2.7E-1

E. 310 x 2.00 410 x 4.00 (as 3 significant figures)

Step #1: 310 x 2.00 410 x 4.00 Given Problem

Step #2: 310 x 2.00

410 x 4.00

Rewrite in correct fraction form

Also, add the +’s to the positive exponent

Step #3: 310

410 x

00.2

00.4

Collect Similar Terms

Step #4:

3 - 4

10 x 00.2 Subtract exponents algebraically

Step #5:

3 4

10 x 00.2 Add exponents algebraically

Step #6: 110x 2.00

Step #7: 110x 2.00

Step #8: Computer Form = 2.00E1

F. 1-10 x 4.61

3-10 x 68.0 (as 3 significant figures)

Step #1: 1-10 x 4.61

3-10 x 68.0 Given Problem

Step #2: 1-10 x 4.61

3-10 x 110 x 6.80

Step #3: 1-10 x 4.61

3-1

10 x 6.80

Add exponents algebraically

Step #4: 1-10 x 4.61

210 x 6.80

Step #5: 110

-210 x

61.4

80.6 Collect similar terms

Step #6:

1- - 2-

10 x 1.4750542 Round-off and then Subtract exponents algebraically

Step #7:

1 2-

10 x 1.48 Add exponents algebraically

Step #8: 1-10x 1.48

Step #9: Computer Form = 1.48E-1

G.

1- 10 x 4.20

1.00 4 10 x 3.00 3- 10 x 6.20 (as 3 significant figures)

Step #1:

1- 10 x 4.20

1.00 4 10 x 3.00 3- 10 x 6.20 Given problem

Step #2:

1- 10 x 4.20

1.00

1

4 10 x 3.00

1

3- 10 x 6.20

Step #3:

10 14.20 1 1

410 x -310 x 1.00 3.00 20.6

Collect Similar Terms

Convert All Parts into fractions

Step #4: 1-10 x 4.20

410 x -310 x 8.601

Round-off to 3 significant figures

Step #5: 1-10 x 4.20

4 3-

10 x 8.61

Add exponents algebraically

Step #6: 1-10 x 4.20

110 x 8.61

Rewrite 18.6 as 1.86 x 10+1

Step #7: 1-10 x 4.20

110 x 110 x 86.1

Step #8:

1-10 x 4.20

1 110 x 86.1

Step #9: 1-10 x 4.20

210 x 86.1

Step #10: 110

210 x

20.4

86.1

Collect Similar Terms!

Step #11: 1 - 2

10 x 0.4428571

Round-off and then Subtract exponents algebraically

Step#12: 1 2

10 x 0.443

Add exponents algebraically

Step #13: 310 x 0.443

Convert 0.443 into 1-10 x 4.43

Step #14: 310 x 1-10 x 4.43

Step #15:

3 1-

10 x 4.43

Step #16: 210x 4.43

Step #17: 210x 4.43

Step #18: Computer Form = 4.43E2

H.

2 10 x 0 10

4 10 x 111 0

-7

10 x 4 16 2-

10 x 0641 0

4- 10 x 610

.

. . .

. (as 3 significant figures)

Step #1:

2 10 x 0 10

4 10 x 111 0

-7

10 x 4 16 2-

10 x 0641 0

4- 10 x 610

.

. . .

. The given problem!

Step #2:

210 x

110 x 1.00

410 x

1-10 x 1.11

1

-710 x

110 x 1.64

2-

10 x 2-

10 x 6.41

4-10 x

110 x 06.1

Step #3:

2 1

10 x 1.00

41-

10 x 1.11

1

7- 1

10 x 1.64

2- 2-

10 x 6.41

4- 1

10 x 06.1

Step #4:

310 x 1.00

310 x 1.11

1

610 x 1.64

410 x 6.41

310 x 06.1

Step #5:

3

10 x 1.00 1 4-

10 x 6.41

3

10 x 1.11 -6

10 x 1.64 3-

10 x 1.06

Step #6:

310 x

4-10 x 1.00 1 6.41

310 x

-610 x

-310 x 1.11 1.64 1.06

Collect Similar Terms

Convert into one large fraction

Step #7:

3 4-

10 x 41.6

3 6- 3-10 x 1.929624

Step #8: 1-10 x 6.41

-610 x 1.93

Step #9: 110

-610 x

41.6

93.1 Collect Similar Terms!

Step #10: 1- 6-

10 x 0.301092

Round-off and then Subtract exponents algebraically

Round-off and then Add exponents algebraically

Step #11: 1 6-

10 x 0.301

Add exponents algebraically

Step #12: 5-10 x 0.301

Step #13: 5-

10 x 1-

10 x 3.01 Convert 0.301 into 1-10 x 3.01

Step #14: 3.01 x 10(-1)+(-5)

Step #15: 3.01 x 10-6

Step #16: Computer Form = 3.01E-6

YOU HAVE COMPLETED JUST

PART –V OF

SCIENTIFIC NOTATION