Math Unit
The metric system, scientific notation, factor labeling and problem solving
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…

1
1000 mg =__________
g

1600
160 cm = __________
mm

109 g =
0.109
__________
kg

1L=
1000
__________
mL

14000
14 km = __________
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
6.02 𝑥 1023
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
1.51x 104
kg = ____________________ kg
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…

6 x 105
(2x103 cm) x (3x102 cm) = ____________________ cm2
3 x 1012

(9x108 g) ÷ (3x10-4 mL) =
____________________ g/mL
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.
100 𝑐𝑚
1𝑚
=
1𝑚
100 𝑐𝑚
=1
Dimensional analysis is a method of problem-solving 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 value
of the number must increase.
When you convert from a small unit to a large unit, the value
of the number must decrease.
Factor Label Method of Conversion
100 cm = 1 m
1 m = 100 cm
100cm
1
1m
1m
1
100cm
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 hr
1 km
60 min
1 km = 0.62 miles
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?
Problem Solving

It is important to understand what you have, what you
need and how you are going to get it.
Example
The mass of a brick of aluminum is 87 g. If the density of
aluminum is 2.7 g/ml, what is the volume of the brick?
Have
Need
How
Mass=87g
Volume
V=M/D
Density = 2.7 g/mL
D=M/V