1. Measuring in the Metric System
Applications of Chemistry - Metric Conversions
Measuring in the Metric System
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2. Conversion “Starters” For Chemistry
Applications of Chemistry - Metric Conversions
Conversion “Starters” For Chemistry
GOAL: learn to convert, without using a calculator:
milliliters  liters
milligrams  grams
millimeters  centimeters
centimeters  meters
nanometers  meters *
AND to be able to do these conversions
On paper
In your head
*requires comfort working in scientific notation
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3. Applications of Chemistry - Metric Conversions
Metric system review
United Streaming Video
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4. Applications of Chemistry - Metric Conversions
Milliliters (ml) → Liters
Milligrams (mg) → gram
Milliliters (ml) → centiliters
Centimeters (cm) → meters
Nanometers (nm) → meters
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5. Applications of Chemistry - Metric Conversions
“The Facts” :
Essential knowledge for our goal:
1000 milliliters = 1 liter
1000 mL = 1 L
1000 milligrams = 1 gram
1000 mg = 1 g
10 milliliters = 1 centiliter
10 mL = 1 cL
100 centimeters = 1 meter
100 cm = 1 m
0.001 kilometers = 1 meter
10-3 nm = 1 m
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6. The Powers of Ten
From Youtube

8. Applications of Chemistry - Metric Conversions
Scientific Notation
In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very SMALL numbers:
Mass of an electron = kg
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9. Applications of Chemistry - Metric Conversions
Imagine the difficulty of calculating the mass of 1 mole of electrons! kg x
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10. Applications of Chemistry - Metric Conversions
Review:
Scientific notation expresses a number in the form:
M x 10n
n is an integer
1  M  10
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11. Applications of Chemistry - Metric Conversions. 9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
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12. Applications of Chemistry - Metric Conversions
2.5 x 109
The exponent is the number of places we moved the decimal.
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13. Applications of Chemistry - Metric Conversions 1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
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14. Applications of Chemistry - Metric Conversions
5.79 x 10-5
The exponent is negative because the number we started with was less than 1.
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15. Adding and subtracting with scientific notation:
Applications of Chemistry - Metric Conversions
Adding and subtracting with scientific notation:
IF the exponents are the same, we simply add subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106 7
x 106
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16. Applications of Chemistry - Metric Conversions
The same holds true for subtraction in scientific notation.
4 x 106
- 3 x 106 1
x 106
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17. Applications of Chemistry - Metric Conversions
If the exponents are NOT the same, we must move a decimal to make them the same.
4 x 106
+ 3 x 105
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18. Applications of Chemistry - Metric Conversions
Student A
4.00 x 106
NO!
x 105
x 105
43.00
 Is this good scientific notation?
To avoid this problem, move the decimal on the smaller number!
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19. Applications of Chemistry - Metric Conversions
Student B
YES!
4.00 x 106
x 105
.30 x 106
4.30
x 106
 Is this good scientific notation?
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20. Applications of Chemistry - Metric Conversions
A Problem for you…
2.37 x 10-6
x 10-4
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21. Applications of Chemistry - Metric Conversions
Solution…
2.37 x 10-6
x 10-4
x 10-4
3.50 x 10-4
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22. Converting Amounts On Paper
Applications of Chemistry - Metric Conversions
Converting Amounts On Paper
Any amount has TWO PARTS:
The NUMBER (hard to miss)
The UNIT (easy at first to ignore)
To show the setup for a conversion problem, you need:
Conversion factors, preferably memorized
Your starting amount, with UNIT
The UNIT you want your answer to have
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23. Where Conversion Factors Come From
Applications of Chemistry - Metric Conversions
Where Conversion Factors Come From
Conversion factors are math bridges
To get them, you start with facts:
For example:
100 cm = 1 m
And now for the math manipulation:
Divide each side by 100 cm
Conversion factor in its usable form
100 cm = _1 m_
100 cm cm
1 = _1 m_
100 cm
_1 m_
100 cm
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24. It’s ok to flip a conversion factor
Applications of Chemistry - Metric Conversions
It’s ok to flip a conversion factor
_1 m_
100 cm
100 cm
1 m
is the same as
This works because
100 cm = 1 m
And we can manipulate from the right side this time:
Conversion factor in its usable form
100 cm = _1 m_
1 m m
100 cm = 1
1 m
100 cm
1 m
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25. Write your own conversion factors
Applications of Chemistry - Metric Conversions
Write your own conversion factors
Each of your essential facts for this lesson can be used to write TWO conversion factors
Use your essential facts to list the conversion factors NOW
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26. Generic One-Step Conversion Problem Setup
Applications of Chemistry - Metric Conversions
Generic One-Step Conversion Problem Setup
List the given amount (with units)
Set up a “blank” fraction next to it
Put the unit from your given amount in the bottom of the blank fraction
Put the unit you want your answer to have in the top of the blank fraction
GIVEN AMOUNT & UNIT
ANSWER UNIT =
UNIT
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27. Applications of Chemistry - Metric Conversions
Finish the job!
1.2 m
100 cm
GIVEN AMOUNT & UNIT
ANSWER UNIT = 1
UNIT m
Find the conversion factor that matches this second fraction
Put in the numbers and solve!
Example: Convert 1.2 m to cm
Write given amount and unit
Put given unit in the bottom of the next fraction
Put the answer unit in the top
Find the conversion factor:
Solve, cancelling units
Answer = 120 cm
100 cm
1 m
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28. Applications of Chemistry - Metric Conversions
Conversion factors
100 cm = 1 m
or 1 cm = 0.01m
1000mm = 1m
or 1mm = m
1km = 1000 m
or 0.001km = 1 m
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29. Practice These Conversions On Paper
Applications of Chemistry - Metric Conversions
Practice These Conversions On Paper
Use the setup we just described:
765 mg = ? g
0.85 L = ? mL
182 cm = ? m
300 mm = ? cm
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