Mathematical Tool Kit

Homework – Sigs. and Sci. Not. handout

Today you will apply the rules for:

• Significant Digits

• Scientific Notation

Significant Digits

• Why do we need them?– The number of significant figures in a

measurement, such as 2.531, is equal to the number of digits that are known with some degree of confidence (2, 5, and 3) plus the last digit (1), which is an estimate or approximation. As we improve the sensitivity of the equipment used to make a measurement, the number of significant figures increases.

Significant Digits

• Rule #1– Digits from 1-9 are always significant. – How many sig. figs.?

• 1• 111• 96548.99

Significant Digits

• Rule #2– Zeros between two other significant digits

are always significant – How many sigs.?

• 1000• 1001• 1000.0089

Significant Digits

• Rule #3– One or more additional zeros to the right of

both the decimal place and another significant digit are significant.

– How many sigs.?• 1000• 1.9800• 1.00• 10.00

Significant Digits

• Rule #4– Zeros used solely for spacing the decimal

point (placeholders) are not significant.– How many sigs.?

• 1000• .002• .0012009

Significant Digits

• Rule #5– ?When not-significant becomes

significant.?– How many sigs.?

• 1287000• Now how many sigs• 1287000

Significant Digits Summary

1. Digits from 1-9 are always significant.

2. Zeros between two other significant digits are always significant

3. One or more additional zeros to the right of both the decimal place and another significant digit are significant.

4. Zeros used solely for spacing the decimal point (placeholders) are not significant.

Scientific Notation

• Very simply scientific notation helps us to keep extremely tiny numbers and ginormous numbers packaged nice and neat.

• To use scientific notation, a number is broken up into a decimal number between 1 and 10 multiplied by a power of 10.

Scientific Notation

• Put into Sci. Not.

• 0.00000000897g

• 12340000L

• 1.0000000089g

• Take out of Sci. Not.

• 9.78 x 104

• 8.99 x 10-4

DO NOW!!!!!!!! Use Calculator• 1)  4.53 x 105                            2)  1913.0

   + 2.2 x 106                                    -    4.6 x 103  

•  3)  2.34 x 1024                         4)    2.130 x 103

   + 1.92 x 1023                               -  6.6 x 102

•  5) 3.95 x 102/1.5 x 106  

•  6) 4.44 x 107 /2.25 x 105

•                 • 7)  (4.50 x 10-12)(3.67 x 10-12)

Systéme International

Measurements and ConversionsHomework Handout

SI system of measurement

• During the 1960 International Conference on Weights and Measures held in Paris, the SI units were defined and given status.

• SI is based on the metric system, originated by French scientists after the French revolution in 1791.

• The orderliness of this system makes it useful for scientific work, and it is used by scientists all over the world.

SI base units

Why is SI (metric system) so useful to scientists?• One major advantage of the metric system

is that it uses the decimal system, where all units are related to smaller or larger units by dividing or multiplying by 10.

Conversions

• Convert 10g to Kg

• Covert 1000 mL to L

• Convert 14000mm to Km

The Scientific Method

Scientific Method• An orderly method for gaining, organizing, and

applying new knowledge. 1. Recognize a question or a problem.  

2. Make an educated guess–a hypothesis–to answer the question.

3. Predict consequences that can be observed if the hypothesis is correct. The consequences should be absent if the hypothesis is not correct.

4. Do experiments to see if predicted consequences are present.

5. Formulate the simplest general rule that organizes the three ingredients–hypothesis, predicted effects, and experimental findings.

• Put the scientific method to use

– Come up with “ANY” thought, idea, observation, or question and track it through the scientific method.

– You are scientists so think this through and be scientific.

Activity – Scientific Method

• Hypothesis - An educated guess; a reasonable explanation that is not fully accepted as factual until tested over and over again by experiment.

• Fact - A phenomenon about which competent observers can agree.

• Law - A general hypothesis or statement about the relationship of natural quantities that has been tested over and over again and has not been contradicted. Also known as a principle.

• Theory - A synthesis of a large body of information that encompasses well-tested hypotheses about certain aspects of the natural world.