Chapter 3Scientific Measurement

• Qualitative measurements- give results in a descriptive, non-numerical form

• Quantitative measurements- give results in a definite form, as numbers and units.

• Scientific notation- a number is written as the product of two numbers- a coefficient and 10 raised to a power.

Ex: 3.6 x 10^4

• 3.6 represent the coefficient- always greater than or equal to 1 and less than 10

• 4 represents the exponent- indicates how many times the coefficient must be x by 10 to = the original number.

• For numbers greater than 10, the exponent is + and equals the number of places the original decimal point has been moved to the left. Ex: 36000= 3.6x10^4

• For numbers less than 10, the exponent is negative and equals the number of places the original decimal point has been moved to the right. Ex: 0.0081= 8.1x10^-3

• To multiply numbers written in scientific notation, multiply the coefficients and add the exponents.

• Ex: (3.0x10^4)(2.0x10^2)=(3.0x2.0)x 10^(4+2)= 6.0 x 10^6

• To divide numbers written in scientific notation, first divide the coefficients. Then subtract the exponent in the denominator (bottom) from the exponent in the numerator (top).

Multiplication & Division

• Ex: (3.0 x 10^4)/(2.0 x 10^2)= 3.0/2.0 x 10^(4-2)= 1.5 x 10^2

Addition & Subtraction• Before adding or subtracting numbers

written in scientific notation, the exponents must be the same.

• Ex: (5.40 x 10^3) + (6.0 x 10^2)

• Make the exponents the same by choosing one to change

• Ex: (5.40 x 10^3) + (0.60 x 10^3)= 6.0 x 10^3

Accuracy & Precision

• Accuracy- a measure of how close a measurement comes to the actual or true value of whatever is measured.

• Precision- a measure of how close a series of measurements are to one another.

• Ex: playing darts (text pg. 54)

• Good accuracy and good precision if the darts are close to the bulls eye and to one another

• Poor accuracy yet good precision if the darts are far from the bulls eye but close to one another.

• Poor accuracy and poor precision if the darts are far from the bulls eye and from one another.

Accepted value, Experimental value and Percent Error

• Accepted value- the correct value based on reliable references.

• Experimental value- the value measured in the lab.

• Error= experimental value – accepted value (can be + or – value).

• Percent Error=([error]/accepted value) x 100. (will always be +)

Significant figures in measurements

• Include all of the digits that are known, plus a last digit that is estimated

• Measurements must always be reported to the correct number of significant figures.

Rules of Significant Figures

• Every nonzero digit in a measurement is assumed to be significant

Ex: 24.7 meters, 0.743 meter, 714 meters

All have 3 significant figures

• Zeros appearing between nonzero digits are significant

Ex: 7003 meters, 40.79 meters, 1.503 meters all have 4 significant figures

• Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders

Ex: 0.0071 meter, 0.42 meter, 0.000099 meter all have 2 significant figures

*write in scientific notation to get rid of the placeholding zeros

Ex: 7.1 x10^-3, 4.2 X10^-1, 9.9 x10^-5• Zeros at the end of a number and to the right of

a decimal point are always significant

Ex: 43.00 m, 1.010 m, 9.000 m all have 4 significant figures

• Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number.

Ex: 300. m—has one sig.fig. 7000. m—has one sig.fig. 27210. m—has 4 sig.figs.*the zeros are not significant. If the zeros were

known measured values, then they would be significant

Ex: if all of the zeros in the measurement 300 m were significant (not rounded)

Writing the value in scientific notation makes it clear the zeros are significant (3.00 x 10^2)

Significant figures in calculations

• Rounding: less than 5 do not round up, greater than 5 round up

• In addition, subtraction, multiplication, and division, round the answer to the same number of sig.figs. as the measurement with the least amount of sig.figs.

Ex: 12.52 + 349.0 + 8.24 =369.76, the answer should be rounded to 369.8 because 349.0 has the least amount of sig.figs (being one sig.fig. After the decimal point)

Metric System

• Standard system used by scientists

• aka International System of Units (SI)

• Decimal system based on the number 10, multiples of 10

• Used to measure length, volume, mass, density, and temperature

Length • Basic unit is the meter (m)• Metric ruler• 1m= 39.4 inches• 1m=100cm• 1m=1000mm• 1000m=1km• 1x10^-6m=1um(micrometer) or 1x10^6um=1m• 1x10^-9m=1nm(nanometer) or 1x10^9nm=1m• K H D M D C M * * um * * nm L cc g (text pg. 64)

Volume• Amount of space an object takes up• V=LxWxH• Basic unit is the Liter (L) or cm^3, mL• Graduated cylinder is used to measure volume

of liquids or irregular shaped solids by water displacement

• Read water level on graduated cylinder at the meniscus

• Use metric ruler to measure volume of solids: LxWxH

• 1 cubic centimeter= 1 milliliter• 1cubic meter= 1000 Liters• (text pg. 65)

Mass• Amount of matter in an object (remains

constant)• Different from weight- a force that

measures the pull of gravity on a given mass (can change)

• Basic unit Kilogram, gram• Use triple beam balance• 1Kg=2.2lbs.• 1Kg=1000g• 1000Kg=1 metric ton• (text pg. 67)

Density

• Mass per unit volume

• D=M/V

• Units g/cm^3, g/mL

• Density of water= 1g/mL

• Float< 1g/mL < Sink

• Density table on pg. 69

Specific Gravity• The comparison of the density of a substance

with the density of a reference substance at the same temp.

• Common reference substance is water• Specific gravity= density of substance/ density of water • No units because they cancel out

(g/cm^3/g/cm^3)• Hydrometer measures specific gravity of liquid• Hydrometer is a sealed tube with a weight in the

bottom. The higher it floats the higher the specific gravity of the liquid being tested

• Specific gravity measurements (no units)

• Used by physicians to diagnose certain diseases (diabetes)

• Check antifreeze condition in radiator

• Measure acid in an automobile battery

Temperature• Kelvin (K) scale or degrees Celsius

• Use thermometer with degrees Celsius

• 0 degrees Celsius= 273 K

• 100 degrees Celsius= 373K

• Water freezes 0 degrees Celsius or 273K

• Water boils 100 degrees Celsius or 373K

• 0 Kelvin or absolute zero= -273K

• K=Celsius + 273

• C=K - 273

Other SI units

• Time is measured in seconds (s)• Pressure is measured in Pascals (Pa)• Atmospheric pressure is measured in atm

or mm of Hg (Mercury)• Energy is measured in joules (J) or

calories (cal)• Amount of a substance is measured in

moles (mol)• Electric current is measured in ampere (A)