MeasurementMeasurement

A quantity that has both a A quantity that has both a number and a unitnumber and a unit

Scientific NotationScientific Notation

A way of writing either very A way of writing either very large or very small large or very small numbers.numbers.

One number to the left of One number to the left of the decimal point the decimal point multiplied by a power of 10.multiplied by a power of 10.

AccuracyAccuracy A measure of how close a A measure of how close a

measurement comes to the true measurement comes to the true value .value .

To evaluate accuracy your To evaluate accuracy your measurement must be measurement must be compared to the true compared to the true measurementmeasurement

PrecisionPrecision

A measure of how close a A measure of how close a series of measurements are series of measurements are to each other.to each other.

To evaluate precision two or To evaluate precision two or more measurements must be more measurements must be compared to each other.compared to each other.

Determining ErrorDetermining Error

Accepted value – the correct Accepted value – the correct value based on reliable value based on reliable referencesreferences

Experimental value – the Experimental value – the value measured in the labvalue measured in the lab

Error = experimental value Error = experimental value

- accepted value- accepted value

% error = % error = lerrorl lerrorl x 100 x 100

accepted valueaccepted value

Significant Figures (sig figs)Significant Figures (sig figs) in measurements always in measurements always

depend on the instrument depend on the instrument being used for the being used for the measurement.measurement.

include all digits that are include all digits that are known plus one digit that is known plus one digit that is estimated.estimated.

All measured numbers are All measured numbers are significant figures.significant figures.

All non-zero numbers are All non-zero numbers are measured.measured.

Zeros that are acting as Zeros that are acting as place holders are not place holders are not measured.measured.

Is the zero measured?Is the zero measured?

Leading zeros are never Leading zeros are never measured.measured.

Captured zeros are always Captured zeros are always measured.measured.

Trailing zeros are only Trailing zeros are only measured if there is a measured if there is a decimal in the number.decimal in the number.

Measurements must always Measurements must always be reported to the correct be reported to the correct number of sig figs because number of sig figs because calculated answers often calculated answers often depend on the number of sig depend on the number of sig figs in the values used in the figs in the values used in the calculations.calculations.

Significant figures in Significant figures in calculationscalculations

In general a calculated In general a calculated answer cannot be more answer cannot be more precise than the least precise than the least precise measurement from precise measurement from which it was calculated.which it was calculated.

Sig figs in addition and Sig figs in addition and subtractionsubtraction

Round your answer to the Round your answer to the same number of decimal same number of decimal places as the measurement places as the measurement with the least number of with the least number of decimal places.decimal places.

Sig figs in multiplication and Sig figs in multiplication and divisiondivision

Round your answer to the Round your answer to the same number of significant same number of significant figures as the measurement figures as the measurement with the least number of sig with the least number of sig figs.figs.

How many sig figs?How many sig figs?

1.1. 0.05730 meters0.05730 meters2.2. 0.00073 grams0.00073 grams3.3. 8.750 x108.750 x10-2-2metersmeters4.4. 40.007 liters40.007 liters5.5. 1.072 grams1.072 grams6.6. 98,000 meters98,000 meters

Round to 3 sig figsRound to 3 sig figs

1.1. 87.073 meters87.073 meters2.2. 4.3621 x 104.3621 x 1088gramsgrams3.3. 0.0152 meters0.0152 meters4.4. 9009 centimeters9009 centimeters5.5. 0.001775 millimeters0.001775 millimeters6.6. 314.721 grams314.721 grams

Calculate and round correctlyCalculate and round correctly

1.1. 61.2m + 9.35m +8.6m =61.2m + 9.35m +8.6m =2.2. (5.3 x 10(5.3 x 1044) + (1.3 x 10) + (1.3 x 1033) =) =3.3. (9.12 x 10(9.12 x 10-1-1) – (4.7 x 10) – (4.7 x 10-2-2) =) =4.4. 34.61cm -17.3cm =34.61cm -17.3cm =5.5. 14.2g + 8.73g + 0.912g =14.2g + 8.73g + 0.912g =6.6. 349.0m – 12.52m – 8.24m=349.0m – 12.52m – 8.24m=

Calculate and round correctlyCalculate and round correctly

1.1. 7.55m x 0.34m =7.55m x 0.34m =2.2. 2.10cm x 0.70m =2.10cm x 0.70m =3.3. 2.4526m/ 8.4 =2.4526m/ 8.4 =4.4. 22.4cm x 11.3cm x 5.2cm =22.4cm x 11.3cm x 5.2cm =5.5. 8432m/ 12.5 =8432m/ 12.5 =6.6. 1.26 x 101.26 x 1044/ 1.7 x 10/ 1.7 x 10-2-2 = =

International System of Units (SI)International System of Units (SI)

kilogram(kg) measures masskilogram(kg) measures massmeter(m) measures lengthmeter(m) measures lengthkelvin(K) measures temperaturekelvin(K) measures temperaturesecond(s) measures timesecond(s) measures timeMole(mol) measures amountMole(mol) measures amount

VolumeVolume Is a derived unit.Is a derived unit. SI unit of volume is the amount SI unit of volume is the amount

of space occupied by a cube of space occupied by a cube that is 1 m along each edgethat is 1 m along each edge

The liter is a common unit of The liter is a common unit of volume = a cube 10cm on each volume = a cube 10cm on each edge.edge.

TemperatureTemperature

The SI unit is the kelvin. The The SI unit is the kelvin. The Kelvin temperature scale is Kelvin temperature scale is directly related to kinetic directly related to kinetic energy. So zero energy = 0Kenergy. So zero energy = 0K

K = K = ooC + 273C + 273 ooC = K - 273C = K - 273

Conversion FactorsConversion Factors

A ratio of equal A ratio of equal measurements.measurements.

1 meter = 100 centimeters1 meter = 100 centimeters 1 m 1 m , , 100 cm 100 cm

100 cm 1 m100 cm 1 m

Dimensional AnalysisDimensional Analysis

A way to analyze and solve A way to analyze and solve problems using the units, problems using the units, or dimensions , of the or dimensions , of the measurement.measurement.

How many minutes are in How many minutes are in exactly one week.exactly one week.

10080 minutes10080 minutes

An experiment requires An experiment requires that each student use an that each student use an 8.5-cm length of Mg ribbon. 8.5-cm length of Mg ribbon. How many students can do How many students can do the experiment with 570-cm the experiment with 570-cm of ribbon available?of ribbon available?

67 students67 students

ConvertConvert

0.044 km to meters0.044 km to meters4.6 mg to grams4.6 mg to grams0.107 g to centigrams0.107 g to centigrams15 cm15 cm33 to liters to liters7.38 g to kg7.38 g to kg6.72 s to milliseconds6.72 s to milliseconds

The radius of the The radius of the potassium atom is 0.227 potassium atom is 0.227 nm. Express this radius in nm. Express this radius in centimeters.centimeters.

2.27 x 102.27 x 10-8 -8 cmcm

DensityDensity

Is the ratio of an objects Is the ratio of an objects mass to its volume.mass to its volume.

It can also be thought of as It can also be thought of as an equality.an equality.

Density of gold=19.3g/cmDensity of gold=19.3g/cm33

19.3g Au = 1 cm19.3g Au = 1 cm33 Au Au

Gold has a density of 19.3 Gold has a density of 19.3 g/cmg/cm33. What is this density . What is this density in kilograms per cubic in kilograms per cubic meter ?meter ?

1930 kg/m1930 kg/m33

A student finds a shiny A student finds a shiny piece of metal she thinks is piece of metal she thinks is aluminum. She measures aluminum. She measures the mass to be 612 g and the mass to be 612 g and the volume to be 245 cmthe volume to be 245 cm33. . Is the sample aluminum?Is the sample aluminum?

Why or why not?Why or why not?

What is the volume of 4.62 What is the volume of 4.62 g of mercury?g of mercury?

What is the mass of 2.00 L What is the mass of 2.00 L of corn oil?of corn oil?

What is the volume of 1.25 What is the volume of 1.25 kg of air?kg of air?