1. Lecture 1.3 Conversion of Units

2. We have all measured things before, but how would you define it?
Measurement: comparing an unknown quantity to a standard unit (known quantity)
What are some standard unit we use now?

3. How can we convert from one unit to another?
In chemistry, you will have to calculate numbers and convert it into different units
A ‘conversion factor’ is used to convert it between units
The quantity does not change, but the unit does
Ex: 60 minutes vs 1 hour… same quantity but different unit

4. How many minutes are there in 2.5 hours?
In order to solve this, we need to find the ‘conversion factor’
The relationship between hours (the number given) and minutes (the number wanted) is 1 hour=60 minutes

5. So the conversion factor will be written as
1 hour or minutes
60 minutes hour
So which one do I use?
The unit that was Given will always be on the bottom (denominator)
The unit that we Want will always be on the top (numerator)

6. How many minutes are there in 2.5 hours? Step 1: What is Given?
What number is given to you in the problem?
Step 2: What do we Want?
What are we trying to solve?
Step 3: What do we know that connects the two?
What is the relationship between the two?
Step 4: Write it out
Step 5: Calculate

7. 2.5 hours 60 minutes = 150 minutes 1 hour

8. How many seconds are there in 24 hours?
Sometimes, we need to use two conversion factors
We know that 60 sec.=1 min, and 60 min= 1 hour

9. 24 hours 60 minutes 60 seconds 1 hour 1 minute 86400 sec 86000 sec

10. How many seconds are there in 7 hours?
How many hours is 567,000 seconds?
30,000 sec (25200)
158 hrs (157.5)

11. Practice How many cm is 22.5 inches? (1 in.= 2.54 cm)
How many cm is 9 feet? (1 feet=12 inches)
How many feet is 987 cm?
How many cm are there in 4.87 yards? (3ft=1yrd)
How many yards are in 343,000 cm?

12. How to convert between metric units
Many countries came together in 1960 to form an international unit of measurements, called Systeme International (SI), or metric system
Examples:
Mass: Kilogram
Length: Meter
Time: Second
Electric current: Ampere

13. SI units can also be used to measure extremely large or small numbers using prefixes
Instead of saying an atom is meters thick, can say its 10 nanometers
1 “nano” represents 10-9 of a number

14. giga- billion G 109 mega- million M 1,000,000 106 kilo- thousand k
Prefix
Meaning
abbreviation
Numeric value
Exponential Notation
giga-
billion G
1,000,000,000
109
mega-
million M
1,000,000
106
kilo-
thousand k
1,000
103
hecto-
hundred h
100
102
deka-
ten da 10
101
n/a
one 1
deci-
one tenth d
0.1
10-1
centi-
hundredth c
0.01
10-2
milli-
thousandth m
0.001
10-3
micro-
millionth μ
10-6
nano-
billionth n
10-9

15. How to convert between metric units
4.5 meters will be how many millimeters?
Step 1: What is Given?
What number is given to you in the problem?
Step 2: What do we Want?
What are we trying to solve?
Step 3: What do we know that connects the two?
What is the relationship between the two?
Step 4: Write it out
Step 5: Calculate

16. The relationship between meters and millimeters is :
1 meter = 103 millimeter
How did we come up with it?
Ans: Count the number of steps!
The “3” is positive because you are going down three steps

17. 1 2 3 kilo- thousand k 1000 103 hecto- hundred h 100 102 deka- ten da
Prefix
Meaning
abbreviation
Numeric value
Exponential Notation
kilo-
thousand k
1000
103
hecto-
hundred h
100
102
deka-
ten da 10
101
n/a
one 1
deci-
one tenth d
0.1
10-1
centi-
hundredth c
0.01
10-2
milli-
thousandth m
0.001
10-3 1 2 3

18. 4.5 meters 103 millimeters = 4500 mm 1 meter 1256 centimeters will be how many kilometers?

19. 1 5 4 3 2 kilo- thousand k 1000 103 hecto- hundred h 100 102 deka- ten
Prefix
Meaning
abbreviation
Numeric value
Exponential Notation
kilo-
thousand k
1000
103
hecto-
hundred h
100
102
deka-
ten da 10
101
n/a
one 1
deci-
one tenth d
0.1
10-1
centi-
hundredth c
0.01
10-2
milli-
thousandth m
0.001
10-3 5 4 3 2 1

20. 1256 centimeters will be how many kilometers?
The relationship between cm and km is:
1 cm = 10-5 km
The “-5” is negative because you are going up five steps
Quick reasoning test: 105 km does not equal to 1 cm.

21. Practice Convert 253 meters into kilometers Convert 0.0345 hm into cm
Convert 1.02 cm into mm

22. Scientific Notations
Scientific notation can be used to write a small number like , or a large number like
We can write the first number as 2.33 x 10-6 and second number as 8.7 x109
Notice that significant figures are consistent
You move the decimal point to the left if the exponent is negative, to the right if it is positive

23. Scientific notation always follows this rule : N x 10n
N is always a single digit, followed by a decimal point if it needs more significant figures
n is any whole number

24. Practice: write the following in scientific notations
Ans: 3.98 x 106
5100.1
Ans: x 103
23.040
Ans: x 101 or just x 10

25.
Ans: 9.10 x 10-11
Ans: 5.01 x 10-8
Ans: 3 x 10-5
579,000,000,000,000
5.79 x 1014