1. 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

2. 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
= 7.52 x 10-5
5,732, = ?
= ?

3. 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 =
1.2 x 108 =
x 104 = ?
3.704 x 10-6 = ?
Practice Problems Handout

4. 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 error
error x 100%
accepted value

5. 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 oC
99.1 oC oC = -0.9 oC
What is the percent error?
-0.9 oC x 100% = 0.9%
100.0 oC

6. State the results of calculations to the appropriate number of significant figures
Measured 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 calculations
Pg. 56: Figure 3.6

7. Rules for Counting Sig Figs
State the results of calculations to the appropriate number of significant figures
Rules for Counting Sig Figs
Every nonzero digit represented in a measurement is significant.
24.7 m has 3 sig figs
has 4 sig figs
has ? sig figs
has ? sig figs
Zeros appearing between non zero digits are significant.
7003 has 4 sig figs
has 5 sig figs
has ? sig figs
has ? sig figs

8. Rules for Counting Sig Figs
State the results of calculations to the appropriate number of significant figures
Rules for Counting Sig Figs
Zeros ending a number to the right of the decimal point are significant
23.80 has 4 sig figs
has 6 sig figs
1, has ? sig figs
has ? sig figs
Zeros starting a number or ending the number to the left of the decimal point are not counted as significant
16000 has 2 sig figs
has 4 sig figs
870,600 has ? sig figs
has ? sig figs

9. Unlimited number of Sig Figs
State the results of calculations to the appropriate number of significant figures
Unlimited number of Sig Figs
Specific whole numbers that are counted (vs measured) have unlimited numbers of significant figures.
23 people
4 fume hoods
Exactly defined quantities have unlimited numbers of significant figures.
1 minute = 60 seconds
10 mm = 1 cm

10. General Rule for Counting Sig Figs
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

11. Sig Figs in Calculations
State the results of calculations to the appropriate number of significant figures
Sig 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!

12. Sig Fig Practice Problems
How many sig figs in each measurement?
meters meters
meters meter sticks
3. 40,506 meters meters
x 104 meters
unlimited

13. Sig Fig Practice Problems
How many sig figs:
meters meters
meters meters
Round each number to the number of sig figs shown:
meters (4) meters (2)

14. Practice Problems
Round each to 2 sig figs and write in scientific notation.
meters x 108 meters
meters meters
8.71 x x 108 m
1.55 x 10-2 m x 103 m
Go to Sig fig HO

15. 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 m m = m
12.52 has 2 decimal places; has 1 decimal place; 8.24 has 2 decimal places
The answer is rounded off to 1 decimal place = m
Practice problems Pg. 60: 9,10 on over head

16. State the results of calculations to the appropriate number of significant figures
Sig 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 = 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

17. 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

18. Density Solving 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

19. STOP And Test 2014

20. Convert between metric units
Quantity SI Unit Non-SI Unit Instrument
Length meter (m) Ruler
Mass gram (g) Balance
Temperature Kelvin (K) oCelsius Thermometer
Volume cubic meter liter Graduated Cylinder
Buret
Energy joule calorie Calorimeter
Amount of mole
substance

21. Convert between metric units
Metric Prefixes
kilo hecto deka one deci centi milli 1,
(m,g,L)
Mega Micro
1,000, ,000,1
Kids have dropped over dead converting metrics

22. Convert between metric units
Metric Conversions
Moving the decimal point
If the unit is the same, use the saying to move the decimal (KHDODCM)
Convert 4.15 kg to cg:
Start at K and move to c. The decimal will be moved 5 places to the right to give 415,000 cg
Convert 3,470 mL to L:
Start at m and move to o. The decimal will be moved 3 places to the left to give 3.47 L
Convert 3.00 cm to mm:
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!)
Convert 756 g to mL:
Can’t be done due to different units!

23. Metric Practice Problems
Convert the following on your own paper:
1) grams to milligrams
2) kilometers to meters
3) 6089 milliliters to kiloliters
4) convert 12.5 cm3 (centimeter cubed) to ml (milliliter)
Answers: 1) mg 2) 4.56 m 3) kl
4) 12.5 ml = 12.5 cm3 because 1ml = 1cm3

24. 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 dm3 to mL:
0.784 dm3 = 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 3
Convert 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

25. 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.

26. 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

27. Temperature Examples:
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?

28. Temperature Examples:
Liquid nitrogen boils at 77.2 K. What is this temperature in °C? – 273 = -196
Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin? Melting point: = 1234 K, boiling point: = 2485 K