THE METRIC SYSTEM
WHY DO WE USE THE METRIC
SYSTEM?
 Almost all other countries are using the
metric system
 Scientists need a universal way to
communicate data (SI Units)
THE METRIC CONVERSION CHART
(STAIRCASE METHOD)
Kilo
1000 Hecto
units
100 Deka
units
10
To convert to a smaller unit, move
decimal point to the right or
multiply.
Basic
Unit Deci
0.1 Centi
units 0.01 Milli
units 0.001
units
To convert to a larger unit, move
decimal point to the left or divide
units
YouTube - metric conversions
- shortcut method
 Do the following conversions…
 1678 mg to kg’s _____________
 456 liters to ml’s ____________
 6,789,000 mm’s to km’s _____________
 1 liter to dl’s _____________
 45 cm’s to km’s _______________
TRY THIS USING THE STAIRCASE
METHOD
1000 mg = ______ g
Step 1: Determine if you are going to go up or down the ladder.
Step 2: Determine how many steps there are from milligrams to
grams.
Step 3: Move the decimal point the amount of places that was
determined in steps 1 & 2.
TRY THIS USING THE STAIRCASE
METHOD
1000 mg = ______
1 g
Step 1: Determine if you are going to go up or down the ladder.
Step 2: Determine how many steps there are from milligrams to
grams.
Step 3: Move the decimal point the amount of places that was
determined in steps 1 & 2.
TRY THIS USING THE STAIRCASE
METHOD
.15 L = __________ ml
TRY THIS USING THE STAIRCASE
METHOD
.15 L = __________
ml
150
Scientific Notation
A short-hand way of writing
large numbers without
writing all of the zeros.
The Distance From the Sun to
the Earth
93,000,000
Step 1
 Move decimal left
 Leave only one number in front of decimal
Step 2
 Write number without zeros
Step 3
 Count how many places you moved decimal
 Make that your power of ten
The power of
ten is 7 because
the decimal
moved 7 places.
 93,000,000 --Standard Form
 9.3 x 107 ---
Scientific Notation
Practice Problem
Write in scientific notation.
Decide the power of ten.
1) 98,500,000 = 9.85 x 10?
9.85 x 107
2) 64,100,000,000 = 6.41 x 10?
6.41 x 1010
3) 279,000,000 = 2.79 x 10?
2.79 x 108
4) 4,200,000 = 4.2 x 10?
4.2 x 106
More Practice Problems
On these, decide where the decimal will be moved.
1) 734,000,000 = ______ x 108
2) 870,000,000,000 = ______x 1011
3) 90,000,000,000 = _____ x 1010
1) 7.34 x 108
2) 8.7 x 1011
3) 9 x 1010
Complete Practice Problems
Write in scientific notation.
1) 50,000
2) 7,200,000
3) 802,000,000,000
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011
Scientific Notation to
Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
3.40000 --- move the decimal
340,000 in standard form
Write in Standard Form
 6.27 x 106
 9.01 x 104
 6,270,000
 90,100
Significant Figures
•Any digit that is not zero is significant
1.234 kg
4 significant figures
•Zeros between nonzero digits are significant
606 m
3 significant figures
•Zeros to the left of the first nonzero digit are not significant
0.08 L
1 significant figure
•If a number is greater than 1, then all zeros to the right of the
decimal point are significant
2.0 mg
2 significant figures
•If a number is less than 1, then only the zeros that are at the end and
in the middle of the number are significant
0.00420 g
3 significant figures
1.8
How many significant figures are in each
of the following measurements?
24 mL
2 significant figures
3001 g
4 significant figures
0.0320 m3
3 significant figures
6.4 x 104 molecules
2 significant figures
560 kg
2 significant figures
1.8
Significant Figures
Addition or Subtraction
The answer cannot have more digits to the right of the decimal
point than any of the original numbers.
89.332
+ 1.1
90.432
3.70
-2.9133
0.7867
one significant figure after decimal point
round off to 90.4
two significant figures after decimal point
round off to 0.79
If you round off to a “5”, if the next digit is ODD, round up.
If it is EVEN, round down (leave it)!
1.8
Significant Figures
Multiplication or Division
The number of significant figures in the result is set by the original
number that has the smallest number of significant figures
4.51 x 3.6666 = 16.536366
3 sig figs
round to
3 sig figs
6.8 ÷ 112.04 = 0.0606926
2 sig figs
= 16.5
= 0.061
round to
2 sig figs
1.8
Significant Figures
Multiplication or Division
The number of significant figures in the result is set by the original
number that has the smallest number of significant figures
4.51 x 3.6666 = 16.536366
3 sig figs
round to
3 sig figs
6.8 ÷ 112.04 = 0.0606926
2 sig figs
= 16.5
= 0.061
round to
2 sig figs
1.8
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
1.8
Dimensional Analysis Method of Solving Problems
1. Determine which unit conversion factor(s) are needed
2. Carry units through calculation
3. If all units cancel except for the desired unit(s), then the problem
was solved correctly.
How many mL are in 1.63 L?
1 L = 1000 mL
1.63 L x
1000 mL
= 1630 mL
1L
1.63 L x
1L
L2
= 0.001630
1000 mL
mL
1.9
The speed of sound in air is about 343 m/s. What is this
speed in miles per hour?
meters to miles
seconds to hours
1 mi = 1609 m
1 min = 60 s
1 mi
60 s
m
x
x
343
s
1609 m
1 min
1 hour = 60 min
60 min
mi
x
= 767
hour
1 hour
1.9