Chapter 5 - Measurements and Calculations

Measurement - quantitative observation - numerical

Qualitative observation – observation or description

Scientific Notation - expresses a number as a product of a number between 1 and 10 and the appropriate power of ten

320 = 3.2 x 102 0.0005 = 5 x 10-4 400 000 = 4 x 105

If 5200 = 5.2 x 1000 then in scientific notation it equals 5.2 x 103.1000 = 10 x 10 x 10 = 103

If 0.00025 = 2.5 x 0.0001 then in scientific notation it equals 2.5 x 10-4.0.0001 = 0.1 x 0.1 x 0.1 x 0.1 = 10-4 (Negative exponents represent a fraction/reciprocal.)

Unit – tells which scale or standard is being used to represent a measurement

International System or SI system - based on metric system

Length - measures distance - meter (m) Volume – three dimensional space occupied by a substance - liter (L) Mass - quantity of matter present in an object - gram (g)

Prefixes can be added to the base unit to represent size of a quantityKilo- (k) 1000 m = 1 kmHecto- (h) 100 m = 1 hmDeca- (D) 10 m = 1 DmBase 1 m, L, g = 1 m, L, g Substitute any baseDeci- (d) 1 m = 10 dm unit in for mCenti- (c) 1 m = 100 cmMilli- (m) 1 m = 1000 mm

Uncertainty in Measurements – when making a measurement, record all certain numbers plus one uncertain number. Measurements always have some degree of uncertainty.

Accuracy – how close a measured value is to an accepted valuePrecision – how close a series of measurements are to one another

Error – difference between an experimental value and an accepted value

% error = |experimental value – accepted value| x 100%accepted value

Significant Figures - (sig figs, SF) all certain numbers plus first uncertain numbers.

We will be using this method of accounting and representing the amount of uncertainty in any measurement or calculation.

Rules for Counting Significant Figures: 1.) All non-zero numbers are automatically significant 1-9.

2.) Zero’s fall into three categories.a) Leading Zero’s- preceding all non-zero digits NEVER COUNT!

0.000213 = 3 SF0.25 = 2 SF

b) Trapped Zero’s- fall between 2 non-zero digits ALWAYS COUNT! 20202 = 5 SF

40.05 = 4 SFc) Trailing Zero’s- to the right of non-zero numbersonly count IF

there is a DECIMAL POINT.3000 = 1 SF The lack of a decimal point shows the 3 is

estimated.3000. = 4 SF The decimal shows that the last zero is

an estimated value.4.0 = 2SF

3.) Infinite significant figures can occur with certain quantities:a) Definitions 1 m = 100 cm as well as 1 inch =

2.54 cmb) Constants is but not 3.14 because it is an estimatec) Counted Objects 8 slices on pizza, 35 pennies

Rules for Rounding – If the digit to be removed is less than 5, then the

number stays the same. If the digit to be removed is equal or greater than 5, then the number rounds up by one.

Multiplication and Division with Significant FiguresNumber of significant figures is the result of the measurement with the smallest number of significant figures.

4.63 8.46 x 7.5 2.1

Addition and Subtraction with Significant Figures Align the decimal points and carry out the calculation. First column to the right of the decimal with an uncertain number

determines the answer.

6.341 6.791 .789 - 2.41__

+ 4.2__

Multiplication and Division with Scientific Notation and Significant Figures

Multiplication DivisionMultiply the Numbers Divide the NumbersAdd the Exponents Subtract the ExponentsMultiply the Units Divide the UnitsRound the Sig.Figs Round the Sig.Figs.

Example: (3.0 x 103 m) x (2.00 x 102 m)

Addition and Subtraction with Scientific Notation and Significant Figures

Must be to the same power of 10 and the same units so convert to larger exponent (left)

Perform addition or subtract and round to Sig.Figs. Units and exponents stay the same.

Example: (2.3 x 105 m) + (2.20 x 104 m)

Dimensional AnalysisConversion factor- ratio of two parts of the statement that relates the two units

All units will divide out except the unit being converted to in the equivalence statement.

_______ km = 250 m

3.54 g = _____ mg

_____ mL = .542 kL