Measurements and Calculations. Chapter 2

Transcription

1 Measurements and Calculations Chapter 2

2 Scientific Method Section 2-1

3 The Scientific Method The scientific method is a logical approach to solving problems by observing and collecting data, formulating hypotheses (if/then), testing hypotheses, and formulating theories that are supported by data.

4 Observing and Collecting Data Observing is the use of the senses to obtain information. includes data collection, data may be: qualitative (descriptive) quantitative (numerical) A system is matter in a given space that has been selected for study during an experiment or observation.

5 Scientists make generalizations based on the data. Hypotheses Scientists use generalizations about the data to formulate a hypothesis, or testable statement. Hypotheses are often if-then statements.

6 Testing a hypothesis requires experimentation that provides data to support or refute a hypothesis or theory. Testing Hypotheses Controls are the experimental conditions that remain constant. Variables are any experimental conditions that change.

7 Theories A model in science is more than a physical object; it is often an explanation of something can be visual, verbal, or mathematical example: atomic model of matter A theory is a broad generalization that explains a body (lot) of facts or phenomena. example: atomic theory

8 Units of Measurement Section 2-2

9 Quantities are things that have magnitude, size or amount. Ex: length, volume, area, weight, mass Quantities and Units Units are used to describe the amount of something to an already defined size Units have abbreviations Ex: meters (m), liters (L), meters squared (m 2 ), pounds (lb), kilograms (Kg)

10 QUANTITY length UNIT grams Practice time moles area cm 3

11 Quantities to be familiar with Mass - measure of the quantity of matter. Weight - measure of the gravitational pull on matter Length - measure of distance Time Temperature Volume - amount of space occupied by an object Density - ratio of mass to volume, or mass divided by volume

12 SI Measurement Scientists all over the world have agreed on a single measurement system called Le Système International d Unités, abbreviated SI. SI has seven base units most other units are derived from these seven

13 SI Units

14 To make base units bigger or smaller, we can add a prefix. The 6 you need to know are: kilo, hecto, deka, deci, centi, milli Metric Prefixes

15 A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. example: How quarters and dollars are related Conversion Factors Units can be converted from one unit to another using dimensional analysis It is a mathematical technique that allows you to use units to solve problems involving measurements quantity sought = quantity given conversion factor example: the number of quarters in 12 dollars

16 Deriving Conversion Factors You can derive conversion factors if you know the relationship between the unit you have and the unit you want example: conversion factors for meters and decimeters

17 Using Scientific Measurements Section 2-3

18 Accuracy -the closeness of measurements to the correct or accepted value of the quantity measured. Precision and Accuracy Precision -the closeness of a set of measurements of the same quantity made in the same way.

19 Percentage Error Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100

20 Some error or uncertainty always exists in any measurement. Error in Measurement skill of the measurer conditions of measurement measuring instruments

21 A student measures the mass and volume of a substance and calculates its density as 1.40 g/ml. The correct, or accepted, value of the density is 1.30 g/ml.what is the percentage error of the student s measurement? practice

22 Significant figures -all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. Significant Figures

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24 Practice How many sig figs? 28.6 g cm 910 m L kg

25 Sig Figs - Addition and Subtration the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.

26 What is the sum of g and g? Practice Calculate the quantity 87.3 cm cm.

27 Sig Figs - Multiplication and Division the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.

28 What is 2.4 g/ml x ml? practice Calculate the area of a rectangular crystal surface that measures 1.34 mm by mm.

29 Less than 5 à keep the number as it is 4.53 rounded to 2 sig figs rounded to 3 sig figs Rounding Rules rounded to 2 sig figs 3.91 rounded to 2 sig figs 5 or higher à round the number up 8968 rounded to 2 sig figs 6.8 rounded to 1 sig fig x 10-5 rounded to 3 sig figs

30 Conversion Factors and Significant Figures There is no uncertainty in exact conversion factors. Ex: 100 cm = 1 m (assume infinite sig figs) So when converting units, the final answer should have the same number of sig figs as the beginning number.

31 Scientific Notation In scientific notation, numbers are written in the form M 10 n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.

32 Put the number into scientific notation. Practice Put the number into scientific notation.

33 Addition and subtraction These operations can be performed only if the values have the same exponent (n factor). You may have to change one of the numbers so that the exponents match Scientific Notation Addition and Subtraction Add the M numbers and keep the same n factor Practice: kg kg

34 Scientific Notation - Multiplication Multiplication The M factors are multiplied, and the exponents are added algebraically. Practice: ( µm)( µm)

35 Scientific Notation - Division Division The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. Practice: