Chapter 1Understanding the Math in Chemistry

I. What are significant figures/digits?A. Significant figures (digits) are a combination of

certain as well as uncertain numbers.

B. Example: 48.3

Certain value

Estimated

48.2896 (rounded up) 48.3101 (rounded down)

This number could have been the result of

rounding

1. Any digit that is not zero is significant. 1234.56 6 significant figures 1234.56 6 significant figures

2. Zeros between non-zero digits are significant.1002.5 5 significant figures

3. Zeros to the left of the first non-zero digit are not significant.000456 3 significant figures 0.0056 2 significant figures

4. If the number is greater than one (1), then all zeros to the right of the decimal point are significant.

457.12 5 significant figures 400.00 5 significant figures 5. If the number is less than one, then only zeros that are at the end of the

number and between non-zero digits are significant.0.01020 4 significant figures

6. For numbers that do not contain decimal points, the trailing zeros may or may not be significant. In this course assume the digits are significant unless told

otherwise. 1000 1, 2, 3, or 4 significant figures. UNCLEAR assume 4 in calculation 0.0010

2 significant figures 1.000 4 significant figures 7. Assume defined and counted quantities have an unlimited number of

significant figures.

This is the way I learned the sig. fig. rules

This will not be the way I teach it to you!! Here are two simple rules!!

Know them!

Rule #1: If a decimal point is present count from

Left to Right (L R)

Rule #2: If a decimal point is absent count from

Right to Left (L R)

DO NOT START WITH 0

DO NOT START WITH 0

C. Significant Figures RULES

D. Predict the amount of sig. figs in the following:

1. 138.7 4 sig. figs.

2. 100 1 sig. fig.

3.0.00320

3 sig. figs.

4. 0.005 1 sig. figs.

5. 89.0 3 sig. figs.

6. 8902 sig. figs.7.

0.0030

2 sig. figs.

8. 10001 sig. fig.

9. 1000. 4 sig. figs.

10. 10500 3 sig. figs.

II. Scientific NotationA. General Equation: M X 10n

1≤ M <10 n= the number of decimal places moved to get to an acceptable M value

+n= greater than 1

-n = less than 1

Examples:

1. 138.7 Is this an acceptable M?

How many places do you have to move the decimal to get to an acceptable M?

.

Answer: 1.387 X 10 2

2. 100

Answer: 1 X 10 2

# of sig. figs in value must match the # of sig figs in scientific notaion

3. 0.000320

Answer: 3.20 X 10 -4

On your own:

4. 0.0050

5. 89.0

6. 890

7. 0.0030

8. 1000

9. 1000.

10. 10500

Answer: 5.0 X 10 -3

Answer: 8.90 X 101

Answer: 8.9 X 10 2

Answer: 3. 0 X 10 -3

Answer: 1 X 10 3

Answer: 1.000 X 103

Answer: 1.05 X 104

Going backwards

1.50 X 10 2 Move decimal point to Move decimal point to make it larger than 1make it larger than 1 150.

3.5 X 10 -4 Move decimal point to Move decimal point to make it smaller than 1make it smaller than 1

.00035

Rounding Rules

A. Adding and Subtracting Rounding Rules

The answer must contain as many decimal places as the least accurate value (the one with the least #

of decimal places)1. 101

2.1

+ 2.11

2. 15

5

+ 6.12

3.

451.06

- 20.0_____

5. 122.4

0.05

+ 1.000

105.21

L.a

105

26.12

26

431.06

431.1

123.450

123.4 123.5

4.

86.232

- _5.00____

81.232

81.23

Why do you always round up??

If you stand on the scale and it says: 122.5lbs?

Would it be fair to say 123???

I don’t think so!!

B. ODD/EVEN Rule is used when only a 5 is next to the digit you are interested in rounding……

ODD Digit Round up

Even Digit Leave it alone

(EVEN…LEAVIN!!)

Let’s practice rounding to 3 sigs figs.1. 107.5=

2. 112.5=

3. 1.155

4. 9.8451=

5. 854.54=

6. .02545=*round to 1 sig fig

108

112

1.16

9.85

855

.03

C. Multiplication and Division Rules

The answer must contain as many significant figuressignificant figures as

the value with the least number of significant figures

Examples:

1. 35.72 (0.00590)=

2. 6810.2/2.4 =

3. 4450/ 5.00=

4. .3287 (45.2)=

.210748

4 3

.211

2837.58333

5 2

2800

3 3

890How many sig figs?

890.

14.85724

4 3

14.9

So what’s the difference between accuracy and precision?

Precision refers to how closely individual measurements agree with each other.The repeatability of the results.

Accuracy refers to how closely a measured value agrees with the correct value.

accurate(the average is accurate)

not precise

precisenot accurate

accurateand

precise

DENSITYmay affect your

DESTINY!

Is it a compliment if someone says……You’re DENSE!

According to your understanding….

What’s more dense?

A Rock

or

A Sponge

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Ice Cubes or Liquid Water

Ice (H2O(s))

Liquid water (H2O(l))

Water expands

11% when it freezes

Oil

Water

Adding water based food

coloring

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Which one is more dense??

Coke v. Diet Coke

Equation for Density

• The amount of matter in a certain amount of space (volume)

Definition for Density

D=Mass (g)

Volume (ml) or (cm3)

Let’s practice some calculations!

YEAH