Chapter 2Measurement andProblem Solving

What is a Measurement? Quantitative

observation. Comparison to an

agreed upon standard. Every measurement has

a number and a unit.

Scientific Notation Technique used to express very large or very

small numbers.

The sun’sdiameter is

1,392,000,000 m.

An atom’s average diameter is0.000 000 000 3 m.

Scientific Notation Expresses a number as a product of a number

between 1 and 10 and the appropriate power of 10.

The sun’sdiameter is

1.392 x 109 m.

An atom’s average diameter is

3 x 10-10 m.

Scientific Notation The number of places the decimal point is

moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative.

Scientific Notation If the decimal point is moved to the left, the

power of 10 is positive. Sun’s diameter = 1,392,000,000 m = 1.392 x 109 m.

If the decimal point is moved to the right, the power of 10 is negative. Average atom’s diameter = 0.0000000003 m = 3 x 10-10 m.

Scientific Notation1. The World’s population is estimated to be

7,187,000,000 people. Express this number in scientific notation.

2. Express the following numbers in scientific notation: 0.0000671; 72.

3. Express the following numbers in standard notation: 2.598 x 10-7; 9.5 x 104.

Significant Figures Writing numbers to reflect precision.

All measurements have some degree of uncertainty.

Significant Figures

Significant Figures When writing measurements, all the digits

written are known with certainty except the last one, which is an estimate.

Record the certain digits and the first uncertain digit (the estimated number).

45.872

CertainEstimated

Significant Figures All non-zero digits are significant.

1.5 has 2 significant figures. Interior zeros are significant.

1.05 has 3 significant figures. Trailing zeros after a decimal point are

significant. 1.050 has 4 significant figures.

Significant Figures Leading zeros are NOT significant.

0.001050 has 4 significant figures. Zeros at the end of a number without a

written decimal point are ambiguous. 150 has 2 or 3 significant figures—

ambiguous.

Significant Figures A number whose value is known with

complete certainty is exact. Exact numbers have an unlimited number of

significant figures.

Significant Figures in Calculations When multiplying or dividing measurements

with significant figures, the result has the same number of significant figures as the measurement with the fewest number of significant figures.

5.02 × 89.665 × 0.10 = 45.0118 = 45

5.892 ÷ 6.10 = 0.96590 = 0.966

Significant Figures in Calculations When rounding to the correct number of

significant figures, if the number after the place of the last significant figure is: 0 to 4, round down. 5 to 9, round up.

In a series of calculations, carry the extra digits through to the final result and then round off.

Significant Figures in Calculations When adding or subtracting measurements

with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places.

5.74 + 0.823 + 2.651 = 9.214 = 9.21

4.8 - 3.965 = 0.835 = 0.8

Significant Figures in Calculations1. An impossibly regular, paved walkway mysteriously appears

overnight; leading out of Seattle. Careful measurement shows this walkway to be 15,432 meters long and 0.42 meters wide. To the correct number of significant figures, what area is covered by walkway? How would this number change if the walkway were 0.41 meters wide? 0.43 meters wide?

2. By the next morning, this walkway has grown 0.42 meters. To the correct number of significant figures, how long is it now?

Units of Measurement Units tell the standard quantity to which we

are comparing the measured property. Scientists use a set of standard units for

comparing all our measurements.

Units of Measurement The SI System

Quantity Unit SymbolLength meter m

Mass kilogram kg

Time second s

Temperature kelvin K

Units of Measurement Length

Measure of the two-dimensional distance an object covers.

Units of Measurement Mass

Measure of the amount of matter present in an object.

Weight: measure of the gravitational pull on an object.

Units of Measurement All units in the SI system are related to the

standard unit by a power of 10. The power of 10 is indicated by a prefix.

Units of Measurement

Prefix SymbolDecimal

EquivalentPower of 10

mega- M 1,000,000 Base x 106

kilo- k 1,000 Base x 103

deci- d 0.1 Base x 10-1

centi- c 0.01 Base x 10-2

milli- m 0.001 Base x 10-3

micro- m 0.000 001 Base x 10-6

nano- n 0.000 000 001 Base x 10-9

Units of Measurement Volume

Measure of the amount of 3-D space occupied by a substance—a derived unit.

Unit Conversions Dimensional analysis: using units as a guide

to problem solving. A quantity in one unit is converted to an

equivalent quantity in a different unit by using a conversion factor that expresses the relationship between units.

Unit Conversions1. A golfer putted a golf ball 6.8 ft across a

green. How many inches does this represent? How many centimeters?

2. What is the volume of a 1.25 gallon jug in cubic centimeters? Cubic inches?(1 gal = 4 qts; 1 L = 1.057 qts)

Density Mass of substance per unit volume of the

substance.

Volume

MassDensity

DensityVolume vs. Mass of Brass y = 8.38x

0

20

40

60

80

100

120

140

160

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

Volume, cm3

Mas

s, g

Density Volume of a solid can be determined by water

displacement.

Density Density :

solids > liquids > gases

Density1. A certain mineral has a mass of 17.8 g and a volume

of 2.35 cm3. What is the density of this mineral?

2. What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL?

3. Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?

Density

Summary of Topics: Chapter 2 Scientific notation Significant figures Exact numbers, Measured numbers Metric units, prefixes Difference between mass and weight Conversion factors Density; D = m/v