Scientific Measurements. The Scientific Method A Way to Solve a Problem!
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Transcript of Scientific Measurements. The Scientific Method A Way to Solve a Problem!
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Scientific MeasurementsScientific Measurements
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The Scientific Method
A Way to Solve a Problem!
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Key terms
• Hypothesis
• Law or principle
• Fact
• Theory
• Experiment
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Hypothesis
• An educated guess; a reasonable explanation that is not fully accepted as factual until tested over and over again by experiment.
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Law or principle
• A general hypothesis or statement about the relationship of a natural quantities that has been tested over and over again and has not been contradicted.
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Fact
• A phenomenon about which competent observers can agree.
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Theory
• Method and means of solving practical problems by applying the findings of science.
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What is the Scientific Method?
• It is the steps someone takes to identify a question, develop a hypothesis, design and carry out steps or procedures to test the hypothesis, and document observations and findings to share with someone else.
• In other words, it’s a way to solve a problem.
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Scientist have to take the time to think logically when they are investigating a question or problem.
• They break things down into many steps that make sense.
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Scientists develop a question, gather information and form an hypothesis.
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Scientific Investigations
• Science is the methodical exploration of nature followed by a logical explanation of the observations.
• Scientific investigation entails:– planning an investigation– carefully recording observations– gathering data– analyzing the results
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The Scientific Method
• The scientific method is a systematic investigation of nature and requires proposing an explanation for the results of an experiment in the form of a general principle.
• The initial, tentative proposal of a scientific principle is called a hypothesis.
• After further investigation, the original hypothesis my rejected, revised, or elevated to the status of a scientific principle.
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It is a series of steps (not always in this order)• Making observations => question• Formulating hypotheses => answering question
inferring, predicting. • Testing hypotheses. => experimenting,
communicating, collecting data, and measuring. • Formulating theories => Confirming hypotheses
that are supported by data. It includes constructing models, and predicting.
The Scientific Method
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The Steps of the Scientific Method page 4 textbook
• 1- Recognize a question or problem.
• 2- Make an educated guess- hypothesis to the question.
• 3.- Make Prediction statements that explain hypothesis. (Research)
• 4. Perform test or Experiments
• 5- State Conclusion what did your experiment show? Did experiment confirm your hypothesis?
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Application
How does the information you found relate to everyday life?
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Uncertainty in Measurements• A measurement is a number with a unit attached.
• It is not possible to make exact measurements, and all measurements have uncertainty.
• We will generally use metric system units, these include.
– the meter, m, for length measurements
– the gram, g, for mass measurements
– the liter, L, for volume measurements
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Length Measurements• Lets measure the length of a candy cane.
• Ruler A has 1 cm divisions, so we can estimate the length to ± 0.1 cm. The length is 4.2 ± 0.1 cm.
• Ruler B has 0.1 cm divisions, so we can estimate the length to ± 0.05 cm. The length is 4.25 ± 0.05 cm.
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Uncertainty in Length
• Ruler A: 4.2 ± 0.1 cm; Ruler B: 4.25 ± 0.05 cm.
• Ruler A has more uncertainty than Ruler B.
• Ruler B gives a more precise measurement.
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Mass Measurements
• The mass of an object is a measure of the amount of matter it posses.
• Mass is measured with a balance and is not affected by gravity.
• Mass and weight are not interchangeable.
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Volume Measurements• Volume is the amount of space occupied by
a solid, liquid, or gas.
• There are several instruments for measuring volume, including:– graduated cylinder
– syringe
– buret
– pipet
– volumetric flask
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Significant Digits
• Each number in a properly recorded measurement is a significant digit (or significant figure).
• The significant digits express the uncertainty in the measurement.
• When you count significant digits, start counting with the first non-zero number.
• Lets look at a reaction measured by three stopwatches.
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Significant Digits Cont.• Stopwatch A is calibrated to seconds (±1 s),
Stopwatch B to tenths of a second (±0.1 s), and Stopwatch C to hundredths of a second (±0.01 s).
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Significant Digits and Placeholders
• If a number is less than one, a placeholder zero is never significant.
• Therefore, 0.5 cm, 0.05 cm, and 0.005 cm all have one significant digit.
• If a number is greater than one, a placeholder zero is usually not significant.
• Therefore, 50 cm, 500 cm, and 5000 cm all have one significant digit.
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Exact Numbers
• When we count something, it is an exact number.
• Significant digit rules do not apply to exact numbers.
• An example of an exact number: there are 3 coins on this slide.
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Rounding Numbers
• All numbers from a measurement are significant. However, we often generate nonsignificant digits when performing calculations.
• We get rid of nonsignificant digits by rounding off numbers.
• There are four rules for rounding off numbers.
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Rules for Rounding Numbers1. If the first nonsignificant digit is less than 5, drop all
nonsignificant digits.
Example:
A calculator displays 12.846239 and 3 significant digits are justified.
The first nonsignificant digit is a 4, so we drop all nonsignificant digits and get 12.8 as the answer.
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2. If the first nonsignificant digit is greater than or equal to 5, increase the last significant digit by 1 and drop all nonsignificant digits.
A calculator display 12.856239 and 3 significant digits are justified.
The first nonsignificant digit is a 5, so the last significant digit is increased by one to 9, all the nonsignificant digits are dropped, and we get 12.9 as the answer.
Rules for Rounding Numbers
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Rounding Numbers3. a) If the last digit is 5 and is preceded by an odd
number, then the last digit should be increased by . Example: 4.635 is rounded to 4.64
b) If the last digit is 5 but is preceded by an even number, then it stays the same or is rounded down by 1.
Example: 4.625 is rounded to 4.62.
4. If a calculation has two or more operations, retain all nonsignificant digits until the final operation and then round off the answer.
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Adding & Subtracting Measurements
• When adding or subtracting measurements, the answer is limited by the value with the most uncertainty.
5 g
5.0 g
+ 5.00 g
15.00 g
• Lets add three mass measurements.
• The measurement 5 g has the greatest uncertainty (± 1 g).
• The correct answer is 15 g.
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Multiplying & Dividing Measurements
• When multiplying or dividing measurements, the answer is limited by the value with the fewest significant figures.
• Lets multiply two length measurements.
5.15 cm × 2.3 cm = 11.845 cm2
• The measurement 2.3 cm has the fewest significant digits, two.
• The correct answer is 12 cm2.
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Exponential Numbers
• Exponents are used to indicate that a number has been multiplied by itself.
• Exponents are written using a superscript; thus, 2×2×2×2 = 24.
• The number 4 is an exponent and indicates that the number 2 is multiplied by itself 4 times. It is read “2 to the fourth power”.
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Powers of Ten• A power of 10 is a number that results when 10 is
raised to an exponential power.
• The power can be positive (number greater than 1) or negative (number less than 1).
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Scientific Notation• Numbers in science are often very large or very
small. To avoid confusion, we use scientific notation.
• Scientific notation utilizes the significant digits in a measurement followed by a power of ten. The significant digits are expressed as a number between 1 and 10.
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Applying Scientific Notation
• To use scientific notation, first place a decimal after the first nonzero digit in the number followed by the remaining significant digits.
• Indicate how many places the decimal is moved by the power of 10.
– A positive power of 10 indicates that the decimal moves to the left.
– A negative power of 10 indicates that the decimal moves to the right.
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Scientific Notation Continued• There are 26,800,000,000,000,000,000,000
helium atoms in 1.00 L of helium gas. Express the number in scientific notation.
• Place the decimal after the 2, followed by the other significant digits.
• Count the number of places the decimal has moved to the left (22). Add the power of 10 to complete the scientific notation.
2.68 × 1022 atoms
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Another Example• The typical length between two carbon atoms in a
molecule of benzene is 0.000000140 m. What is the length expressed in scientific notation?
• Place the decimal after the 1, followed by the other significant digits.
• Count the number of places the decimal has moved to the right (7). Add the power of 10 to complete the scientific notation.
1.40 × 10-7 m
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• Accuracy = proximity of a measurement to the true value of a quantity.
• Precision = proximity of several measurements to each other.
Accuracy versus Precision
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Summary
• A measurement is a number with an attached unit.
• All measurements have uncertainty.
• The uncertainty in a measurement is dictated by the calibration of the instrument used to make the measurement.
• Every number in a recorded measurement is a significant digit.
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Summary Continued
• Place holding zeros are not significant digits.
• If a number does not have a decimal point, all nonzero numbers and all zeros between nonzero numbers are significant
• If a number has a decimal place, significant digits start with the first nonzero number and all digits to the right are also significant.
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Summary Continued• When adding and subtracting numbers, the answer
is limited by the value with the most uncertainty.
• When multiplying and dividing numbers, the answer is limited by the number with the fewest significant figures.
• When rounding numbers, if the first nonsignificant digit is less than 5, drop the nonsignificant figures…If the number is 5 or more, raise the first significant number by one and drop all of the nonsignificant digits.
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Summary Continued
• Exponents are used to indicate that a number is multiplied by itself n times.
• Scientific notation is used to express very large or very small numbers in a more convenient fashion.
• Scientific notation has the form D.DD × 10n, where D.DD are the significant figures (and is between 1 and 10) and n is the power of ten.
• Accuracy refers to the proximity of a measurement to the true value of a quantity.
• Precision refers to the proximity of several measurements to each other.