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### Significant Figures, Scientific Notation, Unit Conversion, and Unit Magnitudes

Significant Figures

- All non-zero digits are significant. 3971874351298 (13 sig. fig.)
- Zeros which start a number are never significant. 0.35 (2 sig. fig) .0000587 (3 sig. fig)
- Zeros which are between other significant figures are significant. 2348762074003 (13 sf).
- Zeros at the end of a number may be significant, if:
- a decimal has been purposefully placed at the end of the number. 5000. (4 sig. fig) 38000 (2 sig. fig.)
- they follow other known significant figures and the number starts with a decimal. .0057200 (5 sig. fig.)

Practice

- How many significant figures are in each of the following number?
1. 368721

2. 0.453

3. 6704000

4. 60

5. 5700.

Practice and Unit Magnitudes

- Change 2346.2005 to show 5 significant figures.
- Change 6000 to 6 significant figures
- Change 0.00085006 to 1 significant figure
- Change 78.5 to 4 significant figures

Rules for Calculations and Unit Magnitudes

- Addition and Subtraction:
- The number of decimal places in the answer should match the least number of decimal places in the problem
- EX: 54.67 + 54.32 +54.0 + 54.777 + 54 = 271.767
The final answer here is 272

- Multiplication and Division
- The number of significant figures in the answer should match the least number of significant figures in the problem
- EX: 3.0 X 395.2 X 0.002 = 2.3712
The final answer is 2

Rules for Calculations and Unit Magnitudes

- Exact Numbers do not limit the # of sig figs in the answer.
- Counting numbers: 12 students
- Exact conversions: 1 m = 100 cm
- “1” in any conversion: 1 in = 2.54 cm

Practice and Unit Magnitudes

- 7846 X 92437 X 235.649 X 3300
- ANS: 560000000000000

- 583.00÷83
- ANS: 7.0

- 567.000 – 12
- ANS: 555

- 78.00 + 45.6 + 0.00467 + 39.45 + 276.999
- ANS: 440.0

- (350000) X [2.8 ÷ (5.4 - 4.09)]
- ANS: 750000

Scientific Notation and Unit Magnitudes

- Scientific notation is simply a method for expressing, and working with, very large or very small numbers.
- -Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent.
- -EX: 5.67 x103 is the scientific notation for 5670
-5.67 x 105

coefficientbaseexponent

Scientific Notation and Unit Magnitudes

1. The coefficient must be greater than or equal to 1 and less than 10.

2. The base must be 10.

3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. A negative exponent means that the decimal is moved to the left when changing to standard notation.

Converting to Scientific Notation and Unit Magnitudes

- Move decimal until there’s 1 digit to its left.
- -Places moved = exponent.
- Large # (>1) positive exponent
- Small # (<1) negative exponent
- EX: Put 987000000000000000 in scientific notation
- 9.87 x1017

- Practice

EXE and Unit Magnitudes

EXP

EXP

ENTER

EE

EE

Scientific Notation- Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

Type on your calculator:

5.44

7

8.1

4

÷

= 671.6049383

= 670 g/mol

= 6.7 × 102 g/mol

Unit Conversion and Unit Magnitudes

- SI units: The International System of Units (abbreviated SI from the French Systèmeinternational d'unités]) is the modern form of the metric system
- a system of units of measurement devised around seven base units and the convenience of the number ten

Unit Conversion and Unit Magnitudes

- I will give you there conversion factors if you need them in a problem!
- 1 inch = 2.54 cm
- exactly 1 lb = 454 g
- 1 qt = 0.946 L
- 1 mi = 5280 ft
- 1 qt = 2 pt
- 4qt = 1 gal
- 1 ounce = 28.349523 grams

Unit Conversions and Unit Magnitudes

- Convert 3598 grams into pounds.
(exactly 1 lb = 454 g )

ANS: 7.925 lbs

Unit Conversions and Unit Magnitudes

- Convert 231 grams into ounces.
(1 ounce = 28.349523 grams)

ANS:8.15 ounces

Unit Conversions and Unit Magnitudes

- How many gallons are in 5.67 L?
(1 qt = 0.946 L and 4qt = 1 gal)

ANS: 1.50

Unit Magnitudes and Unit Magnitudes

Dimensional Analysis and Unit Magnitudes

- Dimensional Analysis
- A tool often used in science for converting units within a measurement system

- Conversion Factor
- A numerical factor by which a quantity expressed in one system of units may be converted to another system

Dimensional Analysis and Unit Magnitudes

- The “Factor-Label” Method
- Units, or “labels” are canceled, or “factored” out

Dimensional Analysis and Unit Magnitudes

- Steps:
1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

Dimensional Analysis Practice and Unit Magnitudes

How many seconds are in 1.4 days?

Plan: days hr min seconds

1.4 days x 24 hr x 60 min x 60 sec =

1 day1 hr 1 min

120960 sec

120000 sec

Classwork/Homework and Unit Magnitudes

- Start reading chapter 1
- You will need information covered in this chapter to complete the lab on Thursday!