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**Ch.2 Measurements and Calculations**

System – specific portion of matter in a given region of space that has been selected for study during an experiment or observation.

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Scientific Method Hypothesis – testable statement controls – remain constant variable – is changed Model – explanation of how phenomena occur and how data or events are related. Theory – broad generalization that explains a body of facts or phenomena.

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**Accuracy and Precision**

Accuracy – close to the expected value Precision – a number of measurements close to each other.

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**What is more accurate? Graduated cylinder Or Beaker **

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**Significant Figures Indicates how precise a measurement is. rule**

example 1. Zeros between other nonzero digits are significant 50.3 m has three sig figs B s has five sig figs 2. Zeros in front of nonzero digits are not significant. 0.892 kg has three sig figs ms has one sig fig 3. Zeros that are at the end of a number and also to the right of the decimal are significant 57.00 g has four sig figs B kg has seven sig figs 4. Zeros at the end of a number but to the left of a decimal are significant if they have been measured or are the first estimated digit; if not they are NOT significant. 1000 m may contain from one to four sig figs, depending on the precision of the measurement, in this book it will be assumed there is one sig fig. 20 m has one sig fig (scientific notation will indicated sig fig number)

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**Rules for calculating with sig figs**

Type of calculation Rule example Addition or subtraction When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement 97.3 Round off Multiplication or division The final answer has the same number of sig figs as the measurement having the smallest number of sig figs. 123 x 658

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Sig fig practice Perform these calculations following the rules for sig figs. 26 x = ? 15.3 / = ? = ? = ?

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**SI unit – measurements in science**

SI unit – measurements in science. Density = m/v A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm3. calculate the density of aluminum.

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Dimensional analysis – math technique that allows you to use units to solve problems involving measurements. Express a mass of grams in milligrams and in kilograms.

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Percentage Error Calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100. Percentage error = valueexperimental – valueexpected x 100 valueexpected

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Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value. y/x = k /4 = /8 = 0.5 y = kx

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Indirect Proportions Two quantities are inversely proportional to each other if their product is constant. If x and y are inversely proportional to each other, the relationship can be expressed as follows: y ∞ 1/x xy = k

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