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!

Using Significant Figures reflects precision by

estimating the last digit

What is the certain measurement? (52 ml)What is the estimated measurement? (.8 ml)

The instrument determines the amount of precision of the data.

What is the certain measurement here? (62.4 g)What is the estimated measurement here? (.00 g)

Error vs. Mistakes

ERROR• Scientific errors are

caused by INSTRUMENTS

• Scientific measurements vary in their level of certainty

MISTAKES• Mistakes are

caused by PEOPLE

• Misreading, dropping, or other human mistakes are NOT error

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 and Counting Numbers do not have significant digits

Exact numbers are important: they are infinitely valuable.

Counting numbers come only in whole numbers.

There are rules for:multiplication/division

addition/subtraction andcombined equations

Rules for multiplication/division

The 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/subtraction

The 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

4. Round the final answer

Calculations

• Addition/Subtraction

• 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

Round only the final answer in a

series of calculations

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!

• Answer is 6.8 cm2

Divide .005673 L by 2.1 L

Calculator says 0.0027014286

4 sig figs and 2 sig figs

2 it is!

Answer is 0.0027 L

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 These

1. 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

How to do problems with scientific notationEx. 4.7 x 10 25 x 1.9 x 10 -13

first do numbers: 4.7 x 1.9

estimate as 5 x 2 = 10

now do powers: 1025 x 10-13

25 + -13 = 12

so 10 x 1012 or 1.0 x 10 13

Calculators can helpFirst, type in the number (ie 4.5)Then press 2nd

Finally, press EE (above the comma)

The number will display as 4.5 E 13Read this as 4.5 x 10 13

Significant figures are easy when using scientific notation

2.3 x 10 25 has 2 sig figs3.7 x 10 -30 has 2 sig figs

The placeholder zeros are eliminated for you!