1. Unit 2:SCIENTIFIC MEASUREMENT
OBJECTIVES (Don’t Copy!)
Convert Between Standard Notation to Scientific Notation
Identify Significant Figures & Uncertainty in Measurements
Perform Operations with Significant Figures
Addition & Subtraction
Multiplication & Division
NOTE: PLEASE COPY EXAMPLES IN THIS SLIDESHOW

2. What is Scientific Notation?
a way of expressing really big numbers or really small numbers.
For some numbers, scientific notation is more concise.

3. Scientific notation consists of two parts:
A number between 1 and 10 (the “coefficient”)
A power of 10
Ex:
7.01
x 108

4. Converting from StandardScientific Notation
EX: Convert 289,800,000 to scientific notation. _______ x 10___
2.898 8
STEP 1: Moving the decimal, convert this number so that it falls between 1 and 10.
STEP 2: Count the number of places you moved the decimal. This is the exponent.
If the number was large to start with, exponent is positive
If the number was small to start with, exponent is negative

5. Examples Given: 0.000567 5.67 x 10 ___ -4 STEP 1 STEP 2
NOTE: This is a very small number, so the exponent is SMALL (negative)
5.67
x 10 ___ -4
___________
STEP 1
STEP 2

6. Converting Scientific Notation to Standard
Ex: x 10 -7
STEP1 : Using the sign on the exponent, decide which way to move your decimal.
Negative sign, move to the left (negative direction)
Positive sign, move to the right (positive direction)
STEP 2: Move the decimal the same number of spaces as the exponent indicates.
Use zeros to hold “empty” spaces.

7. Scientific Notation & Your Calculator
Video Instructions- Using Calculator

8. Plugging Scientific Notation into My Calculator
Find the button on your calculator that is used to enter SCIENTIFIC NOTATION. Write it HERE___ OR
(Do Not Copy) Note: If you find one of the symbols ABOVE a key, rather than ON a key, you must push EE
EXP
2nd EE
2nd
EXP

9. Plugging Scientific Notation Into My Calculator
Ex: Plug this number into your calculator: x 1o-13
(leave the blanks empty for now)
Write the steps you used below
Type 8.93
Push ______ button.
Type_____13_____
Push ____OR____ button
What I see on the screen is _________
NOTE: Use your calculator’s keys if they differ from what is written here EE
NOTE: Sometimes these 2 steps can be reversed
+/-
(-)

10. Scientific Notation: Doing Calculations
Ex: 3 x x 105
USE
CALCULATOR:
Problem
3 x 104 +
2.5 x 105
What you type
3 EE 4
2.5 EE 5
What you see on calculator
304
2.505
NOTE: Use your calculator’s keys if they differ from what is written in table & fill them in
NOTE: Answers must be in scientific notation!
Calculator says:
Correct Answer: 2.8 x 105

11. Practice Calculator says: 0.0521 9.1 x 10-3 + 4.3 x 10-2
ANSWER: 5.21 x 10-2

12. Scientific Notation:Multiplying&Dividing
Ex: (6.1 x 10-3) (7.2 x 109)
USE
CALCULATOR:
Problem
6.1 x 10-3 x
7.2 x 109
What you type
6.1 EE 3-
7.2 EE 9
What you see on calculator
6.1-03
7.209
NOTE: Use your calculator’s keys if they differ from what is written in table
NOTE: Answers must be in scientific notation!
Calculator says:
Correct Answer: x 107

13. In every measurement there is a Number followed by a
Stating a Measurement
In every measurement there is a
Number followed by a
Unit from a measuring device
The number should also be as precise as the measuring device.

14. Ex: Reading a Meterstick
. l I I I I cm
First digit (known) = ?? cm
Second digit (known) = ? cm
Third digit (estimated) between
Length reported = cm
or cm
or cm

15. Significant Figures
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated digit

16. Shortcuts to Sig Figs
The Atlantic-Pacific Rule says: "If a decimal point is Present, ignore zeros on the Pacific (left) side. If the decimal point is Absent, ignore zeros on the Atlantic (right) side. Everything else is significant."

17. Counting Significant Figures: Unlimited Sig Figs
2 instances in which there are an unlimited # of sig figs.
Counting. Ex: 23 people in our classroom.
Exactly defined quantities. Ex: 1hr = 60 min.
Both are exact values. There is no uncertainty.
Neither of these types of values affect the process of rounding an answer.

18. Learning Check (Do Not Copy)
A. Which answers contain 3 significant figures?
1) ) ) 4760
B. All the zeros are significant in
1) ) ) x 103
C. 534,675 rounded to 3 significant figures is
1) ) 535, ) 5.35 x 105

19. Learning Check (Do not copy)
In which set(s) do both numbers contain the same number of significant figures?
1) and 22.00
2) and 40
3) and 150,000

20. Counting Significant Figures: Non-Zero Digits DON’T COPY
RULE 1. All non-zero digits in a measured number ARE significant.
#of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
m ___

21. Counting Significant Figures: Leading Zeros DON’T COPY
RULE 2. Leading zeros in decimal numbers are NOT significant.
#of Significant Figures
0.008 mm 1
oz 3
lb ____
mL ____

22. Counting Significant Figures: Sandwiched Zeros DON’T COPY
RULE 3. Zeros between nonzero numbers ARE significant. (They can not be rounded unless they are on an end of a number.)
# of Significant Figures
50.8 mm 3
2001 min 4
0.702 lb ____
m ____

23. Counting Significant Figures: Zeros @ the End of a # & to the Right of a Decimal
DON’T COPY!
RULE 4. Trailing zeros at the end of a number and to the right of a decimal numbers ARE significant.
# of Significant Figures
43.00 m
yr 5
1.10 gal ____
g ____

24. Counting Significant Figures: Trailing Zeros DON’T COPY
RULE 5. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders.
# of Significant Figures
25,000 in. 2
200. yr 3
48,600 gal ____
25,005,000 g ____

25. Rounding With Sig Figs
When rounding an answer, determine which is the last significant figure. This is where you will round your number.
If the digit immediately to the right of the last sig fig is less than 5, the value of the last sig fig remains the same.
34, 231 rounded to 3 sig figs 
If it is 5 or greater, round up.
Ex: rounded to 3 sig figs 
34,200
0.0925

26. Practice Rounding (p 69)
Round off each measurement to the number of sig figs shown in parentheses.
meters (four)
meter (two)
8792 meters (two)
25,599 (four)
= meters
= meter
NOTE: The zeros are IMPORTANT place holders, but are not SIGNIFICANT b/c they don’t contribute to the precision of the answer.
= 8800 meters
= x 10 4
NOTE: Sometimes the only way to show sig figs properly is to use scientific notation!

27. Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing
If you must round to obtain the right # of sig figs, do so after all calcs are complete

28. Adding and Subtracting
The answer is rounded to the same PLACE as the LEAST PRECISE measurement .
one decimal place
two decimal places
26.54
answer one decimal place

29. Learning Check
In each calculation, round the answer to the correct number of significant figures.
A =
1) ) ) 257
B =
1) ) ) 40.7

30. Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.
Ex: 4.31 cm x 7.22 cm x 9 cm = cm3
= 300 cm3
3 SF
3 SF
1 SF
1 SF

31. Learning Check
A X 4.2 =
1) ) )
B ÷ =
1) ) ) 60
C X =
X 0.060
1) ) )

32. Practice in Teams Q#1: 8.3lb ÷ 9.102 in2 = 0.911887497 = 0.91 lb/in2
2 SF
4 SF
ANSWER: 2 SF

33. Practice in Teams Q#2: 63.2 m2 - 2.38 m2 = 11.05617161 m 5.501 m
3 SF
Q#2: m m2
= m
5.501 m
3 SF
= 11.1 m
4 SF
You only round once! (YORO).
DON’T round after you subtract, then AGAIN after you divide.
Answer: 3 SF
NOTE: When you have a mixture of +/- & x/÷, the rule for x/÷ is used. This rule says, “round to the same # of SF as the measurement with the least # of SF.”

34. You Practice: SF Review WS (Don’t Copy)
#21, 22, 25,27,30,31,32,35,36,37,38,39 (12 problems)

35. M D V ÷ X D = _M_ V (Mass) (Density) (Volume) Density = __Mass__
Cover the variable you are solving for and perform the operation with the given amounts
NOTE: Put this
on your P. Table M
D = _M_ V
(Mass) ÷ D V X
(Density)
(Volume)

36. Common Units for Density Probs (Copy onto P. Table)
Volume = L (mL), cm3
NOTE: 1 mL = 1 cm3
Mass = g (kg, mg, etc.), lbs

37. Density Practice Problem #1 (p 91)
QUESTION: A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?
SOLUTION:
Givens: Unknown:
mass = 3.1 g density = ?
Volume = 0.35 cm3
Find equation and solve D = m/v
D = 3.1 g /0.35 cm3
D = g/cm3

38. Density Practice Problem #2 (p 92)
What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is g/cm3.
Givens: Unknown:
Mass = 14 g volume = ?
Density = 10.5 g/cm3
Find formula & derive it: D = M/V V = M/D
Substitute values & solve V = g
10.5 g/cm3

39. UNITS OF MEASUREMENT
We use SI units — based on the metric system (SI means Systeme Internationale)
Length
Mass
Volume
Time
Temperature
Meter, m
Kilogram, kg
Liter, L
Seconds, s
Celsius degrees, ˚C
kelvins, K

40. Metric Prefixes
Base unit (100) goes here
(g, m, L)

41. How to set up conversion factors in the metric system
If you always select the larger of the 2 units as your “1” unit,
Then the multiplier (on prefixes table) will have a positive exponent.
Ex 1: Compare Megagrams & grams. Which is larger?
Megagrams
This is our “1” unit
1 Mg = 106 grams
This is the multiplier from our table

42. Ex: Compare meters & millimeters
Which is the larger of the 2 units?
meters
This is your “1” unit
NOTE: when you look on your prefixes chart, the “milli-” multiplier is When we use the method of making the larger unit the “1” unit, we always have a positive exponent for our multiplier.
1 meter =
103 mm

43. Conversion Factors Example: 1 km = 103 m Factors: 1 km and 103 m
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: km = 103 m
Factors: 1 km and m
103 m km
They don’t change the value of the measurement, just the units in which it is expressed.

44. Conversion Factors Example: 1 hr. = 60 min Factors: 1 hr. and 60 min
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: hr. = 60 min
Factors: 1 hr and min
60 min hr.
They don’t change the value of the measurement, just the units in which it is expressed.

45. Ex 1: How many millimeters in 1205 meters?
4. Place units of the unknown in the numerator of the conversion factor. (if you can find a relationship between the 2 units. We can! 1m = 103 mm)
1. Identify your given. Place it far left.
1205 m
103 mm m
= _____mm
1.205 x106 1
2. Identify your unknown. Place it far right.
(The given units are in the NUMERATOR. Your goal is to get rid of the units of your given. How?)
5. Cancel units & do the math! (Sig figs!)
3. Place the units of the given in the denominator of the conversion factor!

46. Ex: Convert your weight from pounds (lbs) to kg.
4. Place units of the unknown in the numerator of the conversion factor. (if you can find a relationship between the 2 units. We can! 1kg = 2.2lb)
1. Identify your given. Place it far left. kg 1
150 lbs
lbs
= _____kg 68
2.2
2. Identify your unknown. Place it far right.
The given units are in the NUMERATOR. Your goal is to get rid of the units of your given. How?
5. Cancel units & do the math! (Sig figs!)
3. Place the units of the given in the denominator of the conversion factor!

47. Ex 3: How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x min = min
1 hr
cancel
By using dimensional analysis, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

48. How many seconds are in 1.4 days? Unit plan: days hr min seconds
Example #4: PLEASE COPY
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x 24 hr x _60min x s =___s
1 day hr min
ANSWER: 120,960 s.
FINAL ANSWER (in sig figs) = 120,000 s