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Measuring in the Metric System

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Presentation on theme: "Measuring in the Metric System"— Presentation transcript:

1 Measuring in the Metric System
Applications of Chemistry - Metric Conversions Measuring in the Metric System L Chedid

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 L Chedid

3 Applications of Chemistry - Metric Conversions
Metric system review United Streaming Video L Chedid

4 Applications of Chemistry - Metric Conversions
Milliliters (ml) → Liters Milligrams (mg) → gram Milliliters (ml) → centiliters Centimeters (cm) → meters Nanometers (nm) → meters L Chedid

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 L Chedid

6 The Powers of Ten From Youtube

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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 L Chedid

9 Applications of Chemistry - Metric Conversions
Imagine the difficulty of calculating the mass of 1 mole of electrons! kg x ??????????????????????????????????? L Chedid

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 L Chedid

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 L Chedid

12 Applications of Chemistry - Metric Conversions
2.5 x 109 The exponent is the number of places we moved the decimal. L Chedid

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 L Chedid

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. L Chedid

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 L Chedid

16 Applications of Chemistry - Metric Conversions
The same holds true for subtraction in scientific notation. 4 x 106 - 3 x 106 1 x 106 L Chedid

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 L Chedid

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! L Chedid

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? L Chedid

20 Applications of Chemistry - Metric Conversions
A Problem for you… 2.37 x 10-6 x 10-4 L Chedid

21 Applications of Chemistry - Metric Conversions
Solution… 2.37 x 10-6 x 10-4 x 10-4 3.50 x 10-4 L Chedid

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 L Chedid

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 L Chedid

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 L Chedid

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 L Chedid

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 L Chedid

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 L Chedid

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 L Chedid

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 L Chedid


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