Basic Mathematical Skills in
Chemistry
Mr. Chapman
Chemistry 20
Chemistry is Math!

In chemistry, we have to do a lot of math.

None of the math is super complicated, but it is
important that you learn some basic rules that
we will use for the next two years in chemistry
courses.

There are also some conventions and important
notation that we have to get used to.
The International System of Units (or Systeme
Internationale) is basically an international
language used by scientists to communicate
quantities and measurements.
Units are CRITICALLY IMPORTANT

When you write a number, you need to get used to
one, simple fact.
A NUMBER IS MEANINGLESS WITHOUT UNITS

For instance, let’s say I walk up to you and say this:
“Hey, I have 500 of water.”

What does that mean?!?!?

NOTHING
Four Important SI Units:

Although there are more SI units than this,
these 4 will the most important to us:
FOUR IMPORTANT SI UNITS IN CHEMISTRY:
Quantity
SI Base Unit
English Equivalent
Length
Meter (m)
1 m = 39.36 in
Mass
Kilograms (kg)
1 kg = 2.2 lbs
Time
Seconds (s)
Temperature
Degrees Kelvin (K)
°F = 1.8(oC)+32
K = °C + 273.15
Note: many people screw up the SI unit for mass. The SI unit for mass is kg, which
means 1000 g. Lots of people think this means the SI unit for mass is grams; ITS NOT.
Quick Practice

1.
2.
3.
4.
Write the following numbers with the proper
units:
One thousand seconds
Three hundred degrees Kelvin
Two decimal five four grams
Thirty two metres
Scientific Notation

Scientists often make use of a special way of expressing large and small numbers.
The numbers are expressed in terms of powers, or exponents, of 10. Only one real
number is allowed to be placed to the left of the decimal place when a number is
expressed in scientific notation.
1. Convert these numbers, which are written in exponential notation, to ordinary
expanded notation.
a. 1 x 102_______________________
b. 4.56 x 10-3___________________
c. 9.65 x 106____________________
d. 6.45 x 1012___________________
e. 8.56 x 10-4____________________
f. 6.60 x 100____________________
Scientific Notation Continued...
2. Convert the following numbers into exponential notation.
a. 0.01________________________
b. 10 000 ______________________
c. 0.000 000 0001 _______________
d. 100 _________________________
e. 0.000 2 _____________________
f. 1 ___________________________
3. Re-write the following numbers in correct scientific notation form:
a. 856.3 x 10-3__________________ b. 0.005 x 102____________________
c. 44.32 x 105__________________ d. 99 x 101_______________________
Unit Conversions

There is an old school way to convert between
units, and a big kid way that we are going to
learn in this class. Here is old school:
From top to bottom, the
metric ladder goes in the
following order:
Mega
(106)
Kilo
(103)
Hecto
(102)
Deca
(101)
Base
(100)
Deci
(10-1)
Centi
(10-2)
Milli
(10-3)
Micro
(10-6)
Use the Old-School Method to Convert These Units:
1. 470 ml = _______ L
2. 2000 L = _______ kL
3. 83 g = _______ kg
4. 41300 L = _______ kL
5. 5340 mg = _______ g
6. 2000 m = _______ km
7. 13200 kg = _______ g
8. 1000000 g = _______ kg 9. 320 ml = _______ L
10. 12 L = _______ ml
11. 800 L = _______ kL
12. 250 cm = _______ m
Conversion Factors: The Big Kid Way

Conversion factors are the most important and
useful way to convert between different units.

A conversion factor shows the relationship
between two units. For instance, 1km = 1000m,
so the conversion factor is:
1000 m
1 km
OR
1 km
1000 m
Conversion Factors Continued...
When you use a conversion factor, you always
arrange it like this:
Required
Given
 For example, if you want to find how many
metres there are in 5 km, you need to use this
conversion factor:
1000 m
1 km

Convert These Using the Big Kid Conversion Factors:

13. 20 ml = _______ kL
14. 7000 ml = _______ L
15. 72 cm = _______ mm

16. 900 L = _______ ml
17. 65 m = _______ mm
18. 100 cm = _______ m

19. 117 km = _______ m
20. 42 mg = _______ kg
21. 32 m = _______ mm
Those Others Were Too Easy...

A man has 17284 logs of wood. He knows that
he can bundle 4 logs together to make a
complete bundle. How many complete
bundles can he make? Use a conversion
factor.

The density of water is 1 g/mL. If you have
2.68 kg of water, how many mL do you have?
Use conversion factors.
Can you add, subtract, multiply and divide? We’ll see...
SCIENTIFIC ARITHMETIC
Adding and Subtracting with Units ( + - )

When you add and subtract numbers with units
associated with them, the units never change.
Ex: 2 kg + 3 kg = 5 kg

It seems fairly obvious. However, you also need to
know that in order to add two numbers together, they
must have the same units as a result.
Ex: we can’t add 2 m to 3 km unless we make the units
the same.
Multiplying and Dividing with Units ( x / )

When we multiply and divide with units, it gets a little
more complicated because the units also multiply and
divide.
Ex: 2 m x 2 m = 4 m2

As a result, sometimes the units will cancel each other
out, and we have to understand this:
Ex: 4 s x 2 m = 8 m
s
And Finally, The Golden Rule:

For example: 3 x 4.5 x 10 = ?

If you get 140, you broke the golden rule.

If you get 135, you can stay in this class.