The Metric System
SI
SI stands for International System in French
World’s most widely used system of measurement.
SI base units include: kelvin, second, meter, gram, and the mole.
Length
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The distance between two points.
Base Unit: meter (M)
Measured using a metric ruler
Mass
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Amount of matter in a substance
Base unit: Gram g
Measure using a balance.
Temperature
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Measure of the average kinetic energy of a substance.
Base Unit: Celsius (0C) or Kelvin (K)
Measure using a thermometer.
K = C + 273
Time
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Interval between two occurrences
Base unit: S Second
Measured using a stop watch (i.e. phone)
Volume
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Amount of space an object occupies.
Base Unit: Liter (L)
Measured using a metric ruler or a graduated cylinder
Metric Conversions
Metric conversions are used to make large and small values more manageable.
Warm Up: How many seconds are in 50 days? You may use a calculator.
(50 days) x (24 hours/day) x (60 min/hour) x (60 sec/min) = 4,320,000 seconds
6 Conversion Factors You Should Know
mega (M), kilo (k), deci (d), centi (c), milli (m), mico (µ)
1 m = 1,000,000 µm
1 m = 1000 mm
1 m = 100 cm
1 m = 10 dm
1 km = 1,000 m
1 Mm = 1,000,000 m
3 Step Method
Step 1: Start with a “?”. The “?” means “how many”
Example: Convert 152 cm to m becomes
? m = 152 cm
Step 2: Multiply by a conversion factor. A conversion factor is a statement of fact expressed as a fraction equaling
one. We do not want to change the value, so one is the only thing we can multiply by.
Example: 1 m = 100 cm can be rewritten two ways:
1m/100cm or
100cm/1m
Step 3: Use the units to determine if you are supposed to multiply or divide.
? m = 152 cm X 1 m/1cm
The Metric System Practice Problems
1)
Convert 62 kg to grams
 Step 1: ? g = 62 kg
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Step 2: I know that 1g = 1000 kg
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Step 3:
(62 kg) x (1000 g/kg) = 62, 000 kg
2) Convert 580,000 µm to meters
 Step 1: ? m = 580,000 µm
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Step 2: I know that 1,000,000 µm
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Step 3: 580,000 µm (1 m/1,000,000 µm) = 0.58 m
3) Convert 6 Ml to liters
 Step 1: ? l = 6Ml
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Step 2: 1 ML = 1,000,000 L
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Step 3: (6Ml) x (1,000,000 l/1ML) = 6,000,000 L
4) Convert 4876 meters to centimeters
 Step 1: ? cm = 4876 m
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Step 2: 1 m = 100 cm
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Step 3: (4786 m) x (100 cm/1m) = 47,8600 cm
5) Write < or > or = on each blank
 180 mm __<__ 1.8 m
(180 mm) x (1 m/1000 mm) = 0.18 mm
 55 cg __<___ 55000 g
(55 cg) x (1g/100 cg) = 0.55 g

11,000,000 l ___>___ 1.1 kl
(1.1kl) x (1000l/1kl) = 1100 l
Scientific Notation
Convert from scientific notation to decimal
M x 10n
M is a number that is greater than or equal to 1, but less than 10.
Proper or Improper? Place an X to any number that are not in correct scientific notation.
_____ 9.1 x 105
_____ 8 x 10-3
___x__ 0.4 x 106
___x__ 1.8 x 25
___x__ 860 x 10-3
_____ 9.89898989898 x 106
What Does It Mean?
8 x 103 = 8 x 10 x 10 x 10 = 8000
It is easier to “move the decimal”
8.1101x 103 = 8110.1 (move the zero to the right three “hops” for positive exponents)
8.60 x 10-3 = 0.00860 (we move the zero to the left three “hops” for negative exponents)
Convert from scientific notation to decimal
When going from a very large number to scientific notation, count how many “hops” you have to make so that your
final value ends up in correct scientific notation.
Place an X on any incorrect answer:
_____ 9,100,000 = 91 x 105 Correct answer, improper scientific notation
_____ 0.0008 = 0.8 x 10-3 Correct answer, improper scientific notation
_____ 4,300,000 = 4.3 x 106 Correct _
____ 0.000018 = 1.8 x 105 Correct answer, improper scientific notation
_____ 860 = 8.60 x 10-3 Inorrect answer, improper scientific notation
_____ 9898989 = 9.898989 x 106 Correct answer
Scientific Notation Practice
Convert the Following Into Scientific Notation:
910000000 = _____9.1 x 108 ____________
0.244 = _____2.4 x 10-1____________
84343 = ____8.4343 x 104_____________
0.100003000 = _____1.00003 x 10-1____________
2,003,000,000 = ____2.003 x 109_____________
0.9990000000 = ___9.99 x 10-1_____________
Convert the Following Into Decimal Form:
9.1 x 105 = _____910000____________
2.3445 x 103 = _______2344.5__________
8.6 x 10-3 = ___0.0086______________
8.7676 x 10-3 = _____0.0087676____________
943 x 105 = _______94300000__________
5.88 x 10-5 = ___________0.0000588______
EXTRA CREDIT CHALLENGE: Only try this is you want a challenge.
When multiplying in scientific notation, simply multiply the base numbers and add the exponents. Then, convert your
answer into correct scientific notation.
Example: (9 x 105) x (2 x 105) = 18 x 1010 = 1.8 x 1011
Try This: (8 x 106) x (5 x 107) = 40 x 1013 = 4.0 x 1014
When dividing in scientific notation, divide the base numbers and subtract the exponents.
Example: (3.6 x 105) ÷ (2 x 103) = 1.8 x 102
Try This: (4.5 x 1013) ÷ (5 x 107) = 22.5 x 106 = 2.25 x 107
When adding or subtracting in scientific notation, take out of scientific notation, or make the exponents match.
Example: (3 x 105) + (2 x 103) = (300 x 103) + (2 x 103) = 302 x 103 = 3.02 x 105
Try This: (5 x 1013) + (5 x 107) = (5000000 x 107) + (5 x 107) = 5000005 x 107 = 5.000005 x 1013