Chapter 3

Scientific Measurement

3.1 Using and Expressing Measurements

• Measurement is a quantity that has both a number and a unit.

• Measurements are fundamental to the experimental sciences.

• Scientific notation – a number that is written as the product of two numbers: a coefficient and 10 raised to a power.– Ex. – 602,000,000,000,000,000,000,000 = 6.02 x 1023

Scientific Notation

In scientific notation, the coefficient is always equal to or greater than one and less than 10.

Ex. – 6.02 x 1023

coefficient, > 1 < 10

In other words, only one digit in front of the decimal.

Accuracy, Precision, & Error

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

• Precision – a measure of how close a series of measurements are to one another. – Examine figure 3.2 on page 64 in your text.

Determining Error

• Accepted value – correct value based on reliable references.

• Experimental value – value measured in the lab.

• Error – difference between the experimental value and the accepted value.– Error = experimental value – accepted value

Percent Error

• Error can be positive or negative.• The magnitude of error show the amount by which

the experimental value differs from the accepted value.– Thermometer readings

Percent error = the absolute value of the error divided by the accepted value, multiplied by 100.

% error = (error/accepted value) x 100%

Significant Figures(sig figs)

• Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

• The correct number of sig figs must be reported because calculated answers often depend on the number of sig figs in the values used in the calculation.

Rules for Determining Sig Figs

1. Every nonzero digit in a reported measurement is assumed to be significant.

• 24.7 m, 0.743m,714m = 3 sig figs

2. Zeros appearing between nonzero digits are significant.

• 7003m, 40.79m, 1.503m = 4 sig figs

3. Leftmost zeros appearing in front of nonzero digits are not significant.

• 0.0071m, 0.42m,0.000099m = 2 sig figs

Rules for determining sig figs, cont.

4. Zeros at the end of a number and to the right of a decimal point are always significant.

• 43.00m, 1.010m, 9.000m = 4 sig figs

5. 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.

• 300m, 7000m, 27,210m = 1,1,&4 sig figs respectively

Rules for determining sig figs, cont.

6. Two situations in which numbers have an unlimited number of sig figs.

1. If you count 23 items, for example, people in a classroom, then there are exactly 23 people and this value has an unlimited number of sig figs.

Rules for determining sig figs, cont.

2. Involves exactly defined quantities such as those found w/in a system of measurement.

• Example – 60 min = 1 hr or 100cm = 1m

Each of these numbers has an unlimited number of sig figs.

Sig Figs in Calculations

A calculated answer cannot be more precise than the least precise measurement from which it was calculated.

Example – an area of carpet measures 7.7m by 5.4m. You get an answer of 41.48m2.

Even though you got an answer with 4 sig figs, the measurements used in the calculation had only two sig figs. So the answer must also be reported to two sig figs.

Calculating Sig Figs

• Addition & Subtraction– Answer should be rounded to the same number

of decimal places (not digits), as the measurement with the least number of decimal places.

Example – 12.52 meters + 349.0 meters + 8.24 meters = what?

Calculating Sig Figs

• Multiplication & Division– Answer must be rounded to the same number of

sig figs as the measurement with the least number of sig figs.

– Position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements. Only in addition & subtraction problem rounding.

3.2 International System of Units

• The international System of Units (SI) is a revised version of the metric system.

• The five SI base units commonly used by chemists: meter, kilogram, Kelvin, second, and the mole.

• Refer to table 3.1 on page 73.

Units and Quantities

• Units of length (Table 3.3, p. 74)– Meter and its prefixes

• Units of volume (Table 3.4,p. 75)– Liter and its prefixes– Cubic centimeters

• Units of mass (Table 3.5, p. 76)– Gram and its prefixes, especially kilo- & milli-

• Units of temperature – Kelvin = °C + 273

• Units of energy– Joule

Temperature

• Kelvin is an absolute scale.

• There are no negative Kelvin temperatures.– It is incorrect to say degrees Kelvin or Kelvin

degrees.

The zero point on the Kelvin scale, 0 K is called absolute zero.

Energy (Joules)

• The joule (J) and the calorie are common units of energy.

• Energy is the capacity to do work or to produce heat.

• The joule is the SI unit of energy, named after James Prescott Joule, an English physicist.

• One calorie (cal) is the quantity of heat that raises the temperature of 1g of pure water by 1°C.– 1 J = 0.2390 cal & 1 cal = 4.184 J

3.3 Conversion Factors

Equivalent Measurements– 1 dollar = 4 quarters = 10 dimes = 20 nickels =

100 pennies– 1 meter = 10 decimeters = 100 centimeters =

1000 millimeters

• A conversion factor is a ratio of equivalent measurements.

Conversion Factors

• When measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the measured quantity remains the same.

Dimensional Analysis

• Dimensional analysis is a way to analyze and solve problems using units, or dimensions, of the measurements. – Turn to page 82, sample problem 3.5 for an

example.

Converting Between Units

• Often a measurement needs to be expressed in a unit different from the one given or measured initially.– Turn to page 84 and examine sample problem

3.7.

• Conversion between units often involves more than one conversion factor. – Turn to page 85 and examine sample problem

3.8.

Converting to Complex Units

• More steps must be employed when given a ratio of two units, such as mpg, miles per gallon, or g/cm3.– Examine sample problem 3.9 on page 86.

Sec. 3.4 Density

• Density = mass/volume– Mass = density x volume

– Volume = density/mass

Density of solids & liquids measured in g/cm3

Density of gases measured in g/L

Density is an intensive property that depends on the composition of a substance, not on the size of the sample.

Density & Temperature

Knowns• Mass = 3.1 g• Volume = 0.35 cm3

Unknown• Density = ?g/ cm3

A copper penny has a mass of 3.1 g & a volume of 0.35 cm3. What is the density of copper?

Density of a substance generally decreases as its temperature increases.

Calculate & Evaluate• Solve for the unknown

– D = m/v = 3.1 g/0.35 cm3 =

8.8571 g/cm3 = 8.9 g/ cm3

Conclusion of Ch. 3

• Accuracy and Precision– Accuracy involves the measured value against

the correct value.– Precision involves comparing values of

repeated measurements.

• SI units

• Conversion Factors & Dimensional Analysis

Conclusion of Ch. 3• Significant Figures (Sig Figs)

– Multiplication & Division - answer must be rounded to the same number of sig figs as the measurement with the least number of sig figs

– Addition & Subtraction - answer should be rounded to the same number of decimal places (not digits), as the measurement with the least number of decimal places.

• Density = mass/volume– Mass = density x volume– Volume = density/massDensity is an intensive property that depends only on the composition

of a substance.The density of a substance generally decreases as its temperature

increases.

Questions?