Math Unit
Fill in the blanks in your notes with the words bolded in
purple.
Warm-up Question
The United States is one of how many countries
in the world that still use the imperial system of
measurement?
3
What are the other countries?
• Liberia
• Myanmar
(formerly Burma)
Units of Measurement


SI Units
a system of
units of
measurements
devised around
seven base
units and the
convenience of
the number ten.
Units of Measurement

Metric System
Units of Measurement
Sample problem
Move the decimal to the left
K  h  da  b  d  c  m
Move the decimal to the right
Convert the following
53 hg = ________dg
Start with 53.
Move the decimal 3 spaces to the right
53
Fill in the empty spaces with zeros 53000 dg
Sample Problem
Move the decimal to the left
K  h  da  b  d  c  m
Move the decimal to the right
Convert the following
300 cg = ________kg
Start with 300.
Move the decimal 5 spaces to the left
300
Fill in the empty spaces with zeros 0.00300 kg
Units of Measurement

Examples…

1000 mg =
1
__________
g

160 cm =
1600
__________
mm

109 g =
0.109
__________
kg

1L=
1000
__________
mL

14 km =
14000 m
__________
Move the decimal to the left
K  h  da  b  d  c  m
Move the decimal to the right
Exit Question

Now that you are a metric master, would it be
easier to convert inches to miles or centimeters
to kilometer? Explain.
Warm-up Question

What is the significance of this number?
602000000000000000000000
It’s a mole!!!
(the SI unit for a amount of a substance)
Scientific Notation

Scientific notation expresses numbers as a
multiple of two factors: a number between 1
and 10 (coefficient); and ten raised to a power,
or exponent.



The exponent tells you how many times the first
factor must be multiplied by 10.
When numbers larger than 1 are expressed in
scientific notation, the power of 10 is positive.
When numbers smaller than 1 are expressed in
scientific notation, the power of 10 is negative.
Coefficient
23
6.02 𝑥 10
Exponent
Scientific Notation

Examples…

Change the following data into scientific notation:

The diameter of the Sun is 1,392,000 km.
1.392 𝑥 106 km

The density of the Sun’s lower atmosphere is 0.000000028
g/cm3.
2.8 𝑥 10−8 g/cm3
Scientific Notation

Adding and Subtracting Using Scientific
Notation





The exponents must be the same before doing the
arithmetic. Convert the smaller number to the
bigger one, by moving the decimal to the right.
Add or subtract the coefficient.
Keep the exponent the same.
Make sure your answer is written in proper
scientific notation.
Example…

1.26x104 kg + 2.5x103 kg =
1.51x 10
____________________
kg
4
Scientific Notation

Multiplying and Dividing Using Scientific
Notation



Multiply or divide the coefficients.
Add the exponents (for multiplication) or subtract
the exponents (for division).
Examples…

(2x103 cm) x (3x102 cm) =
6 x 105
____________________
cm2

(9x108 g) ÷ (3x10-4 mL) =
3 x 10
____________________
g/mL
12
Exit Question

Scientific notation should come in handy when
expressing what kinds of quantities in
chemistry?
Submicroscopic things like the size of an atom
or the number of atoms in a substance.
Warm-up Question

How can you simplify this problem before you
calculate the answer?
2
5
×
3
=
4
Dimensional Analysis (Factor Label)

A conversion factor is a ratio of equivalent
values used to express the same quantity in
different units.


A conversion factor is always equal to 1.
Dimensional analysis is a method of problemsolving that focuses on the units used to
describe matter.



Dimensional analysis often uses conversion factors.
When you convert from a large unit to a small unit,
the number of units must increase.
When you convert from a small unit to a large unit,
the number of units must decrease.
Factor Label Method of Conversion
100 cm = 1 m
1 m = 100 cm
100 cm
1
1m
1m
1
100 cm
Use conversion factors to systematically move from
one unit to the next, cancelling out units on the
diagonal in each step.
Convert
18 m = _______ cm
18m
100 cm
1m
= 1800 cm
Dimensional Analysis

Examples…

How many seconds are there in 24 hours?
24 hr

60min
1 hr
60sec
1 min
= 86400 sec
A car is traveling 90.0 kilometers per hour. What is its
speed in miles per minute?
90 km 0.62mi
1 hr
1 km
1 km = 0.62 miles
1 hr
60 min
1 hr = 60 mins
= 0.93 mi/min
1 min = 60 secs
Exit Question
On the planet Rigel, Rigellians have developed a system of
measurements called S.U., or Systems Universal. Here is the
conversion table for the measurements of distance:
1 gleem = 27 blops
1 blop = 34 riddigs
1 riddig = 42 chirks
1 chirk = 9 fuggles
10 fuggles = 52 hippers
2.5 hippers = 1.2 zookas
1 zooka = 7 wenzels
Use the Factor Label Method and the conversions above to solve the
problem.
How many fuggles are there in 19 blops?