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.

Scientific Method

Hypothesis – testable statementcontrols – remain constantvariable – 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.

Accuracy and Precision• Accuracy – close to the expected value• Precision – a number of measurements close

to each other.

What is more accurate?Graduated cylinderOrBeaker

Significant Figures

• Indicates how precise a measurement is.rule example

1. Zeros between other nonzero digits are significant

a. 50.3 m has three sig figsb. B. 3.0025 s has five sig figs

2. Zeros in front of nonzero digits are not significant.

a. 0.892 kg has three sig figsb. 0.0008 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

a. 57.00 g has four sig figsb. B. 2.000000 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.

a. 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.

b. 20 m has one sig fig (scientific notation will indicated sig fig number)

Rules for calculating with sig figsType 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 + 5.85 --------- 103.15 103.2Round off

Multiplication or division The final answer has the same number of sig figs as the measurement having the smallest number of sig figs.

123x 5.35------------- 658.05 658 Round off

Sig fig practice

Perform these calculations following the rules for sig figs.a. 26 x 0.02584 = ?b. 15.3 / 1.1 = ?c. 782.45 - 3.5328 = ?d. 63.258 + 734.2 = ?

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.

Dimensional analysis – math technique that allows you to use units to solve problems involving measurements.

Express a mass of 5.712 grams in milligrams and in kilograms.

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

Direct Proportions

• Two quantities are directly proportional to each other if dividing one by the other gives a constant value.

y/x = k 2/4 = 0.5 4/8 = 0.5

y = kx

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