Chapter 3 Scientific Measurement Understand scientific notation State the results of calculations to the appropriate number of significant figures Convert.

Chapter 3 Scientific Measurement

• Understand scientific notation

• State the results of calculations to the appropriate number of significant figures

• Convert between metric units

• Match units or instruments with the proper measurement

Understand scientific notation

To convert a number into scientific notation;• move the decimal point so only 1 non-zero digit is

to the left of the decimal point. • if you move the decimal point to the left, the

power of 10 will be positive. • if you move the decimal point to the right, the

power of 10 will be negative.3,600 = 3.6 x 103

0.000 075 2 = 7.52 x 10-5

5,732,873.912 = ?0.124 04 = ?

Understand scientific notation

To convert a number out of scientific notation;• if the power of 10 is positive move the decimal

point to the right the power number of places • if the power of 10 is negative move the decimal

point to the left the power number of places.

8.1 x 10-5 = 0.0000811.2 x 108 = 1200000009.342 780 23 x 104 = ?3.704 x 10-6 = ?

Practice Problems Handout

State the results of calculations to the appropriate number of

significant figures

• Accuracy: Measure of how close a measurement comes to the actual or true value

• Precision: Measure of how close a series of measurements are to one another

• Error: Experimental value – accepted

value

• Percent errorerror x 100%

accepted value

State the results of calculations to the appropriate number of

significant figures(Stop: scientific notation and % error problems)

A student measures the temperature

of boiling water. The thermometer

reads 99.1 oC.

What is the error? Accepted value of boiling point of

water is 100.0 oC 99.1 oC - 100.0 oC = -0.9 oC

What is the percent error? -0.9 oC x 100% =

0.9%100.0 oC

State the results of calculations to the appropriate number of

significant figuresMeasured quantities in science have a degree of uncertainty due to

the instrument being used. The measured number has to reflect that uncertainty. That is accomplished by using:

Significant Figures (Sig Figs)

In science, a measured quantity has two meanings:• The numerical value (with the proper units)• The sensitivity (uncertainty) of the measuring instrument:

precision

The number of sig figs is important in calculationsPg. 56: Figure 3.6

State the results of calculations to the appropriate number of

significant figuresRules for Counting Sig Figs

1. Every nonzero digit represented in a measurement is significant.24.7 m has 3 sig figs0.4587 has 4 sig figs134.798 has ? sig figs0.6668 has ? sig figs

2. Zeros appearing between non zero digits are significant.7003 has 4 sig figs0. 96501 has 5 sig figs40.30609 has ? sig figs0.306201 has ? sig figs

State the results of calculations to the appropriate number of

significant figuresRules for Counting Sig Figs

3. Zeros ending a number to the right of the decimal point are significant

23.80 has 4 sig figs0.130700 has 6 sig figs1,006.00 has ? sig figs0.34090 has ? sig figs

4. Zeros starting a number or ending the number to the left of the decimal point are not counted as significant16000 has 2 sig figs0.0002709 has 4 sig figs870,600 has ? sig figs0.0450 has ? sig figs

State the results of calculations to the appropriate number of

significant figures

Unlimited number of Sig Figs

1. Specific whole numbers that are counted (vs measured) have unlimited numbers of significant figures.

23 people

4 fume hoods

2. Exactly defined quantities have unlimited numbers of significant figures.

1 minute = 60 seconds

10 mm = 1 cm

State the results of calculations to the appropriate number of

significant figures

General Rule for Counting Sig Figs

1. Start on the left with the first nonzero digit.

2. End with the last nonzero digit OR with the last zero that ends the number to the right of the decimal point

State the results of calculations to the appropriate number of

significant figuresSig Figs in Calculations

An answer cannot be more precise than the least precise measurement

from which it was calculated!

therefore

Any mathematical calculation involving measured quantities must be

rounded off to reflect the precision of the measurement!

Sig Fig Practice Problems

• How many sig figs in each measurement?– 1. 123 meters 5. 30.0 meters– 2. 0.123 meters 6. 22 meter sticks– 3. 40,506 meters 7. 0.07080 meters– 4. 9.8000 x 104 meters 8. 98000

1. 3 2. 3 3. 5 4. 5 5. 3 6. unlimited7. 4 8. 2

Sig Fig Practice Problems

How many sig figs:1. 0.05730 meters 2. 8765 meters3. 0.00073 meters 4. 1.072 meters1. 4 2. 4 3. 2 4. 4Round each number to the number of sig figs

shown:1. 314.721 meters (4) 2. 0.001755 meters (2)1. 314.7 2. 0.0018

Practice Problems

Round each to 2 sig figs and write in scientific notation.

1. 87.073 meters 2. 4.3621 x 108 meters3. 0.01552 meters 4. 9009 meters1. 8.71 x 101 2. 4.36 x 108 m3. 1.55 x 10-2 m 4. 9.01 x 103 m

Go to Sig fig HO

State the results of calculations to the appropriate number of

significant figures

Sig Figs in Calculations: Addition & Subtraction

• The answer to an addition or subtraction calculation must be rounded to the same number of decimal places as the measurement with the least number of decimal places.

12.52 m + 349.0 m + 8.24 m = 369.76 m 12.52 has 2 decimal places; 349.0 has 1 decimal

place; 8.24 has 2 decimal placesThe answer is rounded off to 1 decimal place = 369.8

mPractice problems Pg. 60: 9,10 on over head

State the results of calculations to the appropriate number of

significant figuresSig Figs in Calculations: Multiplication & Division

• The answer to a multiplication or division calculation must be rounded to the same number of significant figures as the measurement with the least number of significant figures.

7.55 m x 0.34 m = 2.567 m2 7.55 has 3 sig figs; 0.34 has 2 sig figs

The answer must be rounded to 2 sig figs = 2.6 m2

Practice: Pg. 61: Sample Problem 3-4, 11,12

Density

• Density is the ratio of an object’s mass to its volume. Density= Mass/Volume D = m/V units = g/cm3 (solid & liquid) or g/L (gases)

Ex: a piece of lead has a volume of 10.0 cm3 and a mass of 114 g, what is it’s density?114g/ 10.0cm3 = 11.4 g/cm3

DensitySolving for other variables: V = m/D What is the volume of a 68g bar of silver with a

density of 10.5 g/cm3?

M= D x V There are two balloons, 10.0 L each, one

contains helium (D=0.179 g/L), the other contains air (D=1.29g/L). How much less does the helium balloon weigh?

GO TO DENSITY PRACTICE PROBLEM HO

STOP And Test 2014

Convert between metric units

Metric Units Quantity SI Unit Non-SI Unit InstrumentLength meter (m) RulerMass gram (g) BalanceTemperature Kelvin (K) oCelsius ThermometerVolume cubic meter liter Graduated Cylinder

BuretEnergy joule calorie Calorimeter

Amount of mole substance

Convert between metric units

Metric Prefixes

kilo hecto deka one deci centi milli

1,000 100 10 1 0.1 0.01 0.001

(m,g,L)

Mega Micro

1,000,000 0.000,000,1

Kids have dropped over dead converting metrics

Convert between metric units

Metric ConversionsMoving the decimal point

If the unit is the same, use the saying to move the decimal (KHDODCM)

1) Convert 4.15 kg to cg: 1) Start at K and move to c. The decimal will be moved 5

places to the right to give 415,000 cg2) Convert 3,470 mL to L:

1) Start at m and move to o. The decimal will be moved 3 places to the left to give 3.47 L

3) Convert 3.00 cm to mm: 1) Start at c and move to m. The decimal will be moved 1

place to the right to give 30.0 mm (include all sig figs!)4) Convert 756 g to mL:5) Can’t be done due to different units!

Metric Practice Problems

• Convert the following on your own paper:• 1) 34.20 grams to milligrams• 2) 0.00456 kilometers to meters• 3) 6089 milliliters to kiloliters• 4) convert 12.5 cm3 (centimeter cubed) to ml

(milliliter)• Answers: 1) 34200 mg 2) 4.56 m 3) 0.006089 kl• 4) 12.5 ml = 12.5 cm3 because 1ml = 1cm3

Convert between metric units

Volume Measurements & Conversions

Metric volumes come in two forms: Liters or cubic meters

• Conversion between forms: 1 L = 1 dm3 and 1 mL = 1 cm3

Convert 3.45 L to cm3: 3.45 L = 3,450 mL = 3,450 cm3

Convert 0.784 dm3 to mL: 0.784 dm3 = 0.784 L = 784 mL

• Conversion within cubic form: 1 dm3 = 1,000 cm3

When converting within cubic volumes, multiply the number of places the decimal is moved by 3Convert 2.56 m3 to cm3: Move the decimal two places to the right x 3 so a total of 6 places so 2,560,000 cm3 GO to Metric HO

Temperature• Temperature is the measure of kinetic

energy of particles in matter.

• Temperature determines the direction of heat transfer.

• Almost all substances expand with increasing temperature.

Temperature

• The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C.

• The Kelvin scale sets 0 K at absolute zero (the ° symbol is not used).

• One degree on the Kelvin scale is equal to one degree on the Celsius scale.

• 0 K = -273°C 0°C = 273 K K = °C + 273

TemperatureExamples:Liquid nitrogen boils at 77.2 K. What is this

temperature in °C?

Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin?

TemperatureExamples:Liquid nitrogen boils at 77.2 K. What is this

temperature in °C? 77.2 – 273 = -196

Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin? Melting point: 960.8 + 273 = 1234 K, boiling point: 2212 + 273 = 2485 K