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### Introduction to Quantitative ChemistrySignificant FiguresRoundingScientific Notation

Warmup (5 min)

Have your packet out!

1. 103 / 10-4 =

2. (1019) (102) =

3. Round 5.678 to 3 digits

4. 16 =

3.0

5. (56.8)(6.0) =

All answers will be discussed during lecture, but see if you can do these NOW!

*You will need a calculator today.

Take notes on Introduction to Quantitative Chemistry Notes/Problems and ALSO on a separate sheet of paper

Quantitative ObservationsQualitative Observations

Involves measured Involves general

values and numbers observations without

examples? measurement

Ex. It is 36.7⁰C outside today

The river is 31.5 m deep

The cheese costs $4.25 per pound

Ex. It is hot today

The building is tall

I do not weigh a lot

What are significant figures? (‘sig figs’)

“Important numbers”?!?!?!

11.818 sec vs 12.000 sec? Who cares?

In swimming/track, the stopwatch is VERY precise

- There is a reason for placing zeros in a measured value when they are not important for calculation purposes. Significant does not mean IMPORTANT.
- The number of sig figs reported in a value implied the degree of precision of the instrument used to make the measurement.

Which digits are significant?

0.00450600

With a partner, take 2 minutes to discuss how many significant figures are in each of these values:

3

2

1) 1908

2) 0.0025

3) 15.9

5

5

1

4) 0.7040

5) 340.06

6) 140. vs 140.0 vs 140

Pacific Atlanticdecimal present decimal absent

0.00805

100800

4.000100

2000

3

4

7

1

Pick your ocean

Skip zeros, find first 1-9 digit

Count all digits, even the zeros

Round these values to four significant figures:

- 0.0587920 b. 1670.48564 c. 3450824

a. 0.05879 b. 1670. c. 3451000

Rules for Rounding:

- If the digit to be removed is < 5, the preceding digit remains unchanged

Ex. 25.44 rounds to 25.4

- If the digit to be removed is ≥ 5, then the preceding digit is increased by 1

Ex. 25.46 rounds to 25.5

16 = b. (56.8)(6.0) =

3.0

c. 590.0 = d. (324.6)(815.991) =

611

Perform each operation and round answers to the appropriate number of sig figs340

5.3

0.966

264900

Rules1) To see how many sig figs to use in your answer, look at the # sig figs in the values given to you in the problem.2) If the starting values have different numbers of sig figs, use the lower # of sig figs

7.442

- 7.429

0.013

c. 16.82

+ 3.2257

20.0457

20.05

Perform the indicated calculations on the following measured values, giving the final answer with the correct number of significant figures.

- 2.86

+ 3.4921

+ 1.3

7.6521

7.7

Round to the last digit that they have in common. I will sometimes break this rule for one reason or another…… just go with it.

Scientific notation is used to simplify very small or large numbers. It expresses a number as:

- a number between 1 and 10 and

2) a power of 10

Ex. 6780 6.780 x 103

PART 1: Identifying correct scientific notation

Which of these numbers are/are not written in correct scientific notation?

3.57 x 10-8 4.23 x 10-2 75.3 x 10-10

2.92 x 109 0.00345 x 104

Gross!

Move the decimal to the right, exponent = negative

0.00032 3.2 x 10-4

PART 2: Changing a value into scientific notation

Move the decimal to the

left, exponent = positive.

32000 3.2 x 104

a. Change 0.00045 to scientific notation

b. Express 1.28 x 10-5 in standard (regular) notation

a. 4.5 x 10-4 b. 0.0000128

Put the following values into scientific notation using 3 significant figures:

1) 0.00980 3) 25900.0

2) 10.5 4) 0.043

2.59 x 104

9.80 x 10-3

1.05 x 101

4.30 x 10-2

5 x 10-3

4

0.0015

1 x 106

5.05 x 103

0.00000335

220000

2.5 x 10-4

Take 3 minutes to fill in the missing pieces from this chart

PART 3 Multiplying, dividing numbers in scientific notation

Ex A: (2.5 x 105)(2.0 x10-2)

= 5.0 x 103

Ex B: 6.8 x 107

1.7 x 103

****make sure to group values in your calculator using parenthesis!!!!!!!!!!!!!!

= 4.0 x 104 (add a zero bc you need 2 sig figs)

( )

1.78 x 10-11

7.37 x 103

Do the last 5 on your own. I will give answers in 3 minutes.

1. (8.31 x 10-1)(2.14 x10-11) = 2. (3.51 x 10-3)(2.10 x106) =

3. 9.1 x 104 =4. (5.9 x 104) =

11 x 108 (7.2 x 10-3)

5. (5.5 x 104) (1.1 x106) =

(3.2 x 108)

8.2 x 106

8.3 x 10-5

1.9 x 102

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