Significant Figures, and Scientific Notation

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# Significant Figures, and Scientific Notation - PowerPoint PPT Presentation

Significant Figures, and Scientific Notation. The valid measurements or digits are called SIGNIFICANT!. When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.

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### Significant Figures, and Scientific Notation

The valid measurements or digits are called SIGNIFICANT!

When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.
Significant figures are all the digits in a measurement that are known with certainty

plus a last digit that

must be estimated.

Uncertainties of Measurements
• Accuracy is the degree of “exactness” to which the measurement quantity can be reproduced.
Accuracy
• Is the extent to which a measured value agrees with the standard value of the quantity.
• CALCULATORS DO NOT INCREASE THE ACCURACY!

What is the certain measurement? (52 ml)

What is the estimated measurement? (.8 ml)

What is the certain measurement here? (62.4 g)

What is the estimated measurement here? (.00 g)

Error vs. Mistakes

ERROR

MISTAKES

Mistakes are caused by PEOPLE

Misreading, dropping, or other human mistakes are NOT error

• Scientific errors are caused by INSTRUMENTS
• Scientific measurements vary in their level of certainty
Significant Digits
• Nonzero digits are always significant
• All final zeros after the decimal point are significant
• Zeros between two other significant digits are always significant
• Zeros used solely for spacing the decimal point are not significant
Exact numbers are important: they are infinitely valuable. Counting numbers come only in whole numbers.
There are rules for:multiplication/divisionaddition/subtraction andcombined equations

Rules for multiplication/divisionThe result has the same number of significant figures as the factor with the fewest significant figures

The answer can’t be more precise than the question

Rules for addition/subtractionThe result has the same number of decimal places as the number with the fewest decimal places

The answer can’t be more precise than the question

1. Do the functions in parenthesis

2. Note the number of significant digits in the question

3. Perform the remainder of calculations

Calculations
• The answer is based on the number with the fewest decimal points
• Multiplication/Division
• The answer is based on the number with the fewest significant digits
Now You Try It!
• Add 24.686 m +2.343 m + 3.21 m = ?
• Calculator says: 30.239
• 3 decimals, 3 decimals and 2 decimals
• So 2 decimals it is
• Answer is 30. 24 m
• Multiply 3.22 cm by 2.1 cm
• Calculator says 6.762
• 3 sig figs, 2 sig figs . . . So 2 it is!
Divide .005673 L by 2.1 L

Calculator says 0.0027014286

4 sig figs and 2 sig figs

2 it is!

Scientific Notation
• In chemistry we often use very large or very small numbers
• We also have to pay attention to significant figures
• Scientific notation allows us to do both easily!

Scientific Notation is using powers of ten

• 1000 becomes
• 1 X 10 3
• 0.0001 becomes
• 1 X 10 -4
Try These1. 34500 2. 0.00236 3. 56900000 4. 0.0000002386

3.45 x 104

2.36 x 10-3

5.69 x 107

2.386 x 10-7

first do numbers: 4.7 x 1.9

estimate as 5 x 2 = 10

now do powers: 1025 x 10-1325 + -13 = 12

so 10 x 1012 or 1.0 x 10 13

Calculators can help

First, type in the number (ie 4.5)

Then press 2nd

Finally, press EE

(above the comma)

The number will display

as 4.5 E 13

Read this as 4.5 x 10 13

Significant figures are easy when using scientific notation2.3 x 10 25 has 2 sig figs3.7 x 10 -30 has 2 sig figsThe placeholder zeros are eliminated for you!