significant figures & scientific notation significant figures & scientific notation

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Significant Figures Significant Figures & Scientific & Scientific Notation Notation

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Page 1: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Significant Figures & Significant Figures & Scientific Notation Scientific Notation

Page 2: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Rules for Significant Rules for Significant DigitsDigits

1. 1. All non-zero numbers (1-9) are All non-zero numbers (1-9) are significantsignificant (meaning they count as sig figs)(meaning they count as sig figs)

613 = 3 sig figs613 = 3 sig figs 123456 = 6 sig figs123456 = 6 sig figs

2. 2. Zeros located between non-zero digits Zeros located between non-zero digits are ALWAYS are ALWAYS significantsignificant (they count)(they count)

5004 = 4 sig figs5004 = 4 sig figs 602 = 3 sig figs602 = 3 sig figs 6000000000000002 = 16 sig figs!6000000000000002 = 16 sig figs!

Page 3: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

3. 3. Trailing zeros (those at the end) are Trailing zeros (those at the end) are significantsignificant only if the number contains a only if the number contains a decimal pointdecimal point; otherwise they are ; otherwise they are insignificant insignificant (they (they don’t don’t count)count)

55..640 = 4 sig figs640 = 4 sig figs 120000120000.. = 6 sig figs = 6 sig figs 120000 = ONLY 2 sig figs 120000 = ONLY 2 sig figs

4. 4. Placeholder Zeros at the beginning of a Placeholder Zeros at the beginning of a decimal number are decimal number are not not significantsignificant

0.000456 = 3 sig figs0.000456 = 3 sig figs 0.052 = 2 sig figs0.052 = 2 sig figs 0.000000000000000000000000000000000052 = ONLY 2 0.000000000000000000000000000000000052 = ONLY 2

sig figs!sig figs!

Rules for Significant DigitsRules for Significant Digits

Page 4: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Significant figuresSignificant figures are all the digits are all the digits that are that are knownknown in a in a measurementmeasurement, plus , plus the last digit that is the last digit that is estimatedestimated..

The The precisionprecision of a of a calculated calculated answeranswer is is limited by the least limited by the least precise measurement precise measurement used in the used in the calculation.calculation.

Limits of Measurement

Page 5: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Limits of Measurement

Addition & SubtractionAddition & Subtraction::

The solution to the calculation is The solution to the calculation is limited by the least precise limited by the least precise measurement:measurement:

108.536 + 108.536 + 54.54.22 = 162.736 = 162.736 Limited to only Limited to only oneone place past the place past the

decimaldecimal Correct answer = Correct answer = 162.7162.7

Page 6: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Limits of Measurement

Multiplication & DivisionMultiplication & Division::

The solution to the calculation is limited by The solution to the calculation is limited by the measurement with the least number of sig the measurement with the least number of sig figs:figs:

40.9 x 40.9 x 7.27.2 = 294.48 = 294.48 Limited to only Limited to only 22 sig figs sig figs Round the Round the

number number Correct Answer = 290Correct Answer = 290

240/240/66 = 40 = 40 Limited to only Limited to only 11 sig fig sig fig 40 only has 1 sig 40 only has 1 sig

fig (no fig (no decimaldecimal))

Page 7: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Why is scientific notation Why is scientific notation useful?useful?

Using Scientific Notation

Scientists often work with very large or very small numbers.

• Astronomers estimate there are 200,000,000,000 stars in our galaxy.

• The nucleus of an atom is about 0.000000000001 meters wide.

These an be awkward numbers to fully write out and read.

Page 8: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Scientific notationScientific notation expresses a value in two expresses a value in two parts: parts: First part: a number between 1 and 10 First part: a number between 1 and 10 Second part: “10” raised to some powerSecond part: “10” raised to some power

Examples:Examples:

101055 = 10 x 10 x 10 x 10 x 10 = 100,000 = 10 x 10 x 10 x 10 x 10 = 100,000

1010-3-3 = = 11//1010 x x 11//1010 x x 11//1010 = 0.1 x 0.1 x 0.1 = = 0.1 x 0.1 x 0.1 = 0.0010.001

The 2 parts are then multipliedThe 2 parts are then multipliedExample: 5,430,000 = 5.43 x 10Example: 5,430,000 = 5.43 x 1066

Using Scientific Notation

Page 9: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

General Form is: A.BCD… x 10General Form is: A.BCD… x 10QQ

Numbers GREATER that 1 have POSTIVE Numbers GREATER that 1 have POSTIVE Q’sQ’s (exponents) (exponents) Example: Example: 1.23 x 101.23 x 1044 = 12,300 = 12,300

Numbers LESS than 1 have NEGATIVE Numbers LESS than 1 have NEGATIVE Q’sQ’s (exponents) (exponents) Example:Example: 7.6 x 107.6 x 10-5-5 = 0.000076 = 0.000076

Using Scientific Notation

Page 10: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

““Placeholder” zero’s are droppedPlaceholder” zero’s are dropped Placeholders are used between the last non-Placeholders are used between the last non-zero digit and the decimal (even if decimal is zero digit and the decimal (even if decimal is not shown)not shown)

Examples:Examples:

2,5702,570 = 2.57 x 10= 2.57 x 1033

583,000583,000 = 5.83 x 10= 5.83 x 1055

15,06015,060 = 1.506 x 10= 1.506 x 1044

0.00560.0056 = 5.6 x 10= 5.6 x 10-3-3

0.040400.04040 = 4.040 x 10= 4.040 x 10-2-2

Using Scientific Notation

Page 11: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Standard to Scientific Standard to Scientific NotationNotation

1.1. Move the decimal to create a Move the decimal to create a number between 1-10 number between 1-10 (there should (there should never be more than one number to the never be more than one number to the left of the decimal!)left of the decimal!)

Drop any zeros after the last non-zero Drop any zeros after the last non-zero numbernumber

Example: 6,570 Example: 6,570 6.576.57

2.2. Write the multiplication sign and Write the multiplication sign and “10” “10” after the new numberafter the new number

Example: 6.57 Example: 6.57 x 10x 10

Page 12: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

3.3. The number of spaces you moved the The number of spaces you moved the decimaldecimal from its original place to create from its original place to create the new number the new number becomes the becomes the EXPONENTEXPONENT

Example: 6.57 x 10Example: 6.57 x 1033

4.4. If the original number was GREATER than If the original number was GREATER than 1 you are done (the exponent will remain 1 you are done (the exponent will remain positive). positive). If the original number was LESS If the original number was LESS than 1 than 1 (a decimal number) then your (a decimal number) then your exponent will be NEGAVTIVEexponent will be NEGAVTIVE

Example: 0.009605 Example: 0.009605 9.605 x 10 9.605 x 10-3-3

Standard to Scientific NotationStandard to Scientific Notation

Page 13: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Scientific Notation to Scientific Notation to StandardStandard

1.1. Start with the EXPONENT Start with the EXPONENT 5.0903 x 5.0903 x 101055

1.1. Number of spaces & directionNumber of spaces & direction1.1. Positive Exp – ending number greater than Positive Exp – ending number greater than

11

2.2. Negative Exp – ending number less than 1Negative Exp – ending number less than 1

2.2. Move decimal the designated number of Move decimal the designated number of spaces spaces 5.0903 . 5.0903 . 50903_. 50903_.

3.3. Fill in empty spaces with ZERO’s Fill in empty spaces with ZERO’s 509,030.509,030.

Page 14: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Go to Worksheet Go to Worksheet ProblemsProblems

Page 15: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Worksheet ProblemsWorksheet Problems1)1) 46,583,000 =46,583,000 =2)2) 2.0094 x 102.0094 x 103 3 ==3)3) 0.0000945 =0.0000945 =4)4) 4.603 x 104.603 x 1088 = =5)5) 8.0965 x 108.0965 x 10-4-4 = =6)6) 90,294 =90,294 =7)7) 0.000000389 =0.000000389 =8)8) 390 =390 =

4.6583 x 104.6583 x 1077

2,009.42,009.49.45 x 109.45 x 10-5-5

460,300,000460,300,0000.000809650.000809659.0294 x 109.0294 x 1044

3.89 x 103.89 x 10-7-7

3.9 x 103.9 x 1022

Page 16: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Worksheet ProblemsWorksheet Problems

9)9) 5.928 x 105.928 x 100 0 ==10)10) 3.872 x 103.872 x 1011 = =11)11) 90,827 =90,827 =12)12) 100 =100 =13)13) 6.392048 x 106.392048 x 10-3-3 = = 14)14) 8,940 =8,940 =15)15) 3.5839 x 103.5839 x 1066 = =16)16) 8.90284 x 108.90284 x 10-4-4 = =

5.9285.92838.7238.729.0827 x 109.0827 x 1044

1 x 101 x 1022

0.0063920480.0063920488.94 x 108.94 x 1033

3,583,9003,583,9000.0008902840.000890284

Page 17: Significant Figures & Scientific Notation Significant Figures & Scientific Notation

Worksheet ProblemsWorksheet Problems17)17) 67,290 =67,290 =

18)18) 0.000027 =0.000027 =

19)19) 0.001435 =0.001435 =

20)20) 8.9 = 8.9 =

21)21) 409 =409 =

22)22) 3.0293 x 103.0293 x 1044 = =

23)23) 1.0012 x 101.0012 x 10-1-1 = =

24)24) 50,903 = 50,903 =

6.729 x 106.729 x 1044

2.7 x 102.7 x 10-5-5

1.435 x 101.435 x 10-3-3

8.9 x 108.9 x 1000

4.09 x 104.09 x 1022

30,29330,293

0.100120.10012

5.0903 x 105.0903 x 1044