Intro to Science, Measurements, Data

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Intro to Science

How does Science happen?1. Observation2. Identify Problem3. Investigation/Research4. Formulate Hypothesis5. Experimentation6. Collect Data7. Conclusion

◦Does this sound familiar?

Intro to Science

Variables tested during experimentation◦Independent Variable – the variable that is

changed during an experiment ◦Dependent Variable – the variable that is

dependent on the change in the experiment◦Control Group – The group that receives no

change to see what would happen naturally without experiment

◦Experiment Group – The group that receives the factors of experiment to test the change in results

It is possible to study the sciences and gain some appreciation and understanding of it without mathematics.

However, the depth of your comprehension of chemistry is directly related to your math skills. The topics we are about to review are essential math skills that you should master before studying chemistry. lt is critical that you seek tutoring at any time you do not understand a topic in this unit.

Intro to Science

Mathematics can be used to measure many laws. ◦Quantitative measurements – Measurements

that contain a numerical amount of evidence. ◦Qualitative measurements – Measurements that

contain an observable amount of evidence. Tell which is which:

1. The apple is more red than the other.2. The man is twice as fast as the dog. 3. The iron contains 1,500kJ less heat than the

Aluminum.

Intro to Science

In order to make the graphs and charts we need, we use numerical data.

Metric System◦System of organized, alike measurements that

can be related to one another along a simple scale.

SI Units◦Formal units used for types of measurements in

science. ◦Developed by the French!

Intro to Science

Found on pg. 34-35 in your text

Intro to Science

How do we get the best result from our measurements?Accuracy vs. Precision

◦Accuracy – A measurement that is close to the accepted value.

◦Precision – A set of measurement results that are consistent with one another

II. Kinds of numbers

II. Kinds of numbers

Intro to Science

In lab you measured the volume during 4 trials and got 23 cm3, 26 cm3, 21 cm3, 22 cm3

◦If the accepted value should have been 25 cm3, then were your measurements accurate? Were they precise?

◦What is a reason you might have gotten more than the accepted value?

Kinds of numbers

II. Kinds of NumbersB. Counting numbers

◦1. numbers that you count (duh)a. are number without units b. are known exactly

examples: you are holding 5 pens; there are 29 students in

the class

Kinds of numbers

1. Defined numbers a. are numbers that somebody defined to be true b. are known exactly

examples: 16 oz = 1 lb.; 2.54 cm = 1 in; 12 in = 1 ft

Kinds of numbers

3. Measured numbers a. are obtained with a measuring

device ex: yard stick, balance

b. measured numbers are not known exactly; there is a limit to how many digits you can obtain when

measuring.

Kinds of numbers

4. Practice identifying numbers:

a. What kind of number is “3 people”? counting

b. What kind of number is 1 quart?

defined

II. Kinds of numbers

4. Practice identifying numbers:

While jogging to school this morning, you pass 3 people each drinking 1 quart of orange juice.

counting (3 people) defined (1 quart)

MATH REVIEW

I. Exponential notation or Scientific notation

◦1. lmportance: makes expressing very large and very small numbers easier

MATH REVIEW

2. Standard Scientific Notation: a. has only one number in front of a

decimal point [or an understood decimal point]

b. converting to standard notation

MATH REVIEW

Report the following numbers in scientific notation:

a. 20,000

b. 543.6 c. 0.000005

2 X 104

5.436 X 102

5 X 10-6

What are Significant Digits?

III. Significant digits (sig figs)

A. Significant digits are all digits that are known with some

degree of accuracy

What are Significant Digits?

1. Counting numbers and defined numbers have an infinite number of significant digits because they

involve no doubt

a. there are 29 people in the class

b. there are 12 inches in a foot

What are Significant Digits?

B. Identifying Significant Digits

1. all non zero numbers are significant

2. middle zeros are significant (sandwich rule)

III. What are Significant Digits?

3. leading zeros are never significant

a. they are important but not significant (measured)

b. leading zeros are only place holders

III. What are Significant Digits?

4. trailing zeros are significant if there is a decimal point

a. If a number is expressed in scientific notation, the zeroes are removed without affecting the value of the number

III. What are Significant Digits?

All of the following measurements have 3 significant digits.

245 m 18.0 g

308 km 0.00623 g

Which of the rules explains why these numbers all have 3 significant digits?

III. What are Significant Digits?

C. Calculations Using Significant Digits

1. Rounding a. look one place past the last sig fig b. if it is five or more round up c. if it is less than five do not round

What are Significant Digits?

Self Test Round the following numbers to three significant digits, then to one.

87.073 m 4.3621x 108 m 0.01552 m 9009 m 1.7777 x 10-3 m 629.55 m

87.1 m 4.36x108 m 0.0155 m9010 m1.78x10-3m 630. m

90 m4x108 m0.02 m9000 m 2x10-3m 600 m

III. What are Significant Digits?

2. Adding & Subtracting: round answers to the least number of places after the decimal in the numbers you are adding or subtracting

III. What are Significant Digits?

ExampleIf you were adding :

25.3 123.789 +22.45 _____________

The calculator answer would be 171.539.

However, the answer would be correctly reported as 171.5 because 25.3 only has one place beyond the decimal, meaning it was the least precise of the measurements.

What are Significant Digits?

Self Test: a. 61.2m + 9.35m + 8.6m

79.2m b. 9.44m - 2.111m

7.33m

c. 1.36m+ 10.17m 11.53m

d. 34.61m - 17.3m 17.3m

III. What are Significant Digits?

Solutions:

a. 79.2m b. 7.33m c. 11.53m d. 17.3m

III. What are Significant Digits?

3. Multiplying & Dividing: round answers to the least number of significant diqits in any of the numbers you are multiplying or dividing

III. What are Significant Digits?

ExampleIf you were multiplying:

25.3 X 123.789

The calculator answer would be 3131.8167.

However, the answer would be correctly reported as 3130 or 3.13 X 103 because 25.3 only has 3 significant digits

III. What are Significant Digits?

Self Test:

a. 8.3m x 1.22mb. (1 x 10-3m) (2.9 x 10-2 m) c. 8432m ÷12.5m d. 5.3m ÷ 0.255m

III. What are Significant Digits?

Solutions:

a. 10. m2

b. 3 x 105 m2 c. 675 m d. 21 m

IV. Your Calculator

A. Getting to know your calculator

1. the most important button you’ve never used, the EE or Exp button

IV. Your Calculator

A. Getting to know your calculator 2. the “EE” or “Exp” button basically is shorthand for the words “times ten to the…” so it should be used as such when entering data into your calculator

Important note:Sometimes the “EE” button is on the second row of command buttons

III. What are Significant Digits?

ExampleIf you were multiplying:

(25.3 x 103)X(123.789x10-6)

You would enter “25.3” then “EE” then “3” then “X” then “123.789” then “EE” then “-6” then “=“.

The calculator answer should be 3.1318167.

(Of course, the answer would be correctly reported as 3.13 because 25.3 only has 3 significant digits)

III. What are Significant Digits?

Self Test Perform the following calculations and report the answer with the appropriate number of sig figs.

(1) 87.073 X 4.3621 x 108 (2) 0.01552 X 1.7777 x 10-3 (3) 9009 x 10-3 X 629.55 x 108

III. What are Significant Digits?

Self Test answers

(1) 3.7892 x 10-10 (2) 2.759 x 10-5 (3) 1.431 x 10-10