Scientific Notation And

Significant Figures

Scientific Notation

Scientific notation consists of two parts:

A number between 1 and 9A power of 10

N x 10x

* Examples *Given: 289,800,000

Use: 2.898 (moved 8 places)Answer: 2.898 x 108

Given: 0.000567Use: 5.67 (moved 4 places)Answer: 5.67 x 10-4

Learning Check Express these numbers in Scientific

Notation:1) 405789 2) 0.003872 3) 30000000004) .00000002 5) 0.478260

4.05789 x 105

3.872 x 10-3

3 x 109

2 x 10-8

4.7826 x 10-1

Significant Figures

Significant Figures

AKA (also know as):

Sig FigsSignificant Digits

Definition:A method of rounding off

calculated measurements

No answer can be more precise than the least precise measurement

Rounding rules Look at the number

behind the one you’re rounding.

If it is 0 to 4 don’t change it

If it is 5 to 9 make it one bigger

5.87192 Round 2 digits Round 3 digits Round 4 digits

7.9237439 Round 1 digits Round 2 digits Round 4 digits Round 5 digits

Rounding5.9

5.87

5.872

8

7.9

7.924 7.9237

Significant Figures How many numbers mean anything

When we measure something, we can (and do) always estimate between the smallest marks.

21 3 4 5

Significant FiguresThe more marks the better we can

estimate.

Scientist always understand that the last number measured is actually an estimate

21 3 4 5

Significant Figures How do we read the ruler? 4.5515 cm? 4.551 cm? 4.55 cm? 4.5 cm? 4 cm? We needed a set of rules to decide

21 3 4 5

Rules for Working with Significant Figures:

Leading zeros are never significant. Imbedded zeros are always significant. Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.

Addition or Subtraction:The last digit retained is set by the first doubtful digit.

Multiplication or Division:The answer contains no more significant figures than the least accurately known number.

Significant Figure Rules

Rule #1: All real numbers (1, 2, 3, 4, etc.) count as significant figures.

Therefore, you only have to be concerned with the 0

Whether a 0 is significant or not depends on the location of that 0 in the number

Which zeros count?Rule #2: Zeros at the end of a number without a decimal point don’t count12400 g (3 sig figs)

Rule #3: Zeros after a decimal without a number in front are not significant.0.045 g (2 sig figs)

Which zeros count?

Rule #4: Zeros between other sig figs do count.1002 g (4 sig figs)

Rule #5: Zeroes at the end of a number after the decimal point do count45.8300 g (6 sig figs)

Other Information about Sig FigsOnly measurements have sig figs.A a piece of paper is measured 11.0 inches

tall.Counted numbers are exactA dozen is exactly 12Being able to locate, and count significant

figures is an important skill.

Learning Check

A. Which answers contain 3 significant figures?1) 0.4760 cm 2) 0.00476 cm 3) 4760

cm

B. All the zeros are significant in

1) 0.00307 mL 2) 25.300 mL 3) 2.050 x 103

mL

C. 534,675 g rounded to 3 significant figures is1) 535 g 2) 535,000 g 3) 5.35 x 105 g

Learning Check

In which set(s) do both numbers contain the same number of significant figures?

1) 22.0 and 22.00

2) 400.0 and 40

3) 0.000015 and 150,000

4) 63,000 and 2.1

5) 600.0 and 144

6) 0.0002 and 2000

NO

NO

YES- 2

YES- 2

NO

YES-1

How many sig figs in the following measurements?458 g4850. g4850 g0.0485 g0.004085 g40.004085 g

Learning Check

3

4

3

3

4

8

Next we learn the rules for

calculations

Unfortunately, there are different rules for addition and

subtraction and for multiplication and division

Rules forAddition and Subtraction

Your answer must have the same number of digits to the right of

the decimal point as there are in the measurement having the

fewest digits to the right of the decimal point in the problem.

WOW!!! What does that mean?

2.515 cm1.3 cm

+ 12.00 cm

15.815 cmAnswer stops here

Example:

Another Example

First line up the decimal places

Then do the adding Find the estimated

numbers in the problem This answer must be

rounded to the tenths place

If 27.93 mL of NaOH is added to 6.6 mLof HCL, what is the total volume of your

solution?

27.96 mL+ 6.6 mL

34.6 mL

34.56 mL

Rules forMultiplicationand Division

Your answer MUST have the same number of sig figs as the

least

number of sig figs in the

numbers from the problem. What the heck does that

mean?

135 cm x 32 cm = 4320 cm2

3 S.F.3 S.F. 2 S.F.2 S.F. 2 S.F.2 S.F.Round off the answer to 4300

cm3 which is 2 sig figs.

Example:

610 m x 6.20 m = 3782 m2

2 S.F2 S.F.. 3 S.F.3 S.F.What is the correct answer?

3800 m2

Another Example

2 S.F2 S.F..

1. 2.19 m X 4.2 m = A) 9 m2 B) 9.2 m2 C) 9.198 m2

2. 4.311 cm2 ÷ 0.07 cm = A) 61.58 cm B) 62 cm C) 60 cm

3. (2.54 mL X 0.0028 mL) = 0.0105 mL X 0.060 mL

A.) 11.3 mL B)11 mL C) 0.041mL

Learning Check