Problem Solving – a Math
Review
Unit 1
Significant Figures, Scientific
Notation & Dimensional Analysis
Significant Figures
 In science, we describe a value as having a
certain number of significant figures or
digits.
– Includes all the #’s that are certain and 1
uncertain digit (the LAST one).
– There are rules that dictate which #’s are
considered significant!
Rules for Significant Figures
 Any non-zero # is considered significant
 Zeroes!
– Any zeroes between 2 numbers is significant
 Ex. 205 has 3 sig. figs.
 Ex. 4060033 has 7 sig. figs.
 Ex. 10.007 has 5 sig. figs.
– Any zeroes before a number are NOT
significant
 Ex. 0.054 has 2 sig. figs.
 Ex. 0.000 005 has 1 sig. fig.
Rules for Significant Figures
 Zeroes! Continued
– Any zeroes after numbers may or may not be
significant.
 If there is a decimal point in the number, then YES, they are
significant!
– Ex. 12.000 has 5 sig. figs.
– Ex. 0.1200 has 4 sig. figs.
– Ex. 530.0000 has 7 sig. figs.
 If there is no decimal point in the number, then NO, they aren’t
significant!
– Ex. 120 has 2 sig. figs.
– Ex. 430 000 000 000 has 2 sig. figs.
Adding/ Subtracting and Significant
Figures
 The rule
– When adding or subtracting
 Look at the Significant Figures AFTER the decimal
point. Which one has the least amount? That’s how
many significant figures your answer can have
Examples
 17.34 + 4.900 + 23.1 = 45.34
(1 sig. fig after decimal) = 45.3
 9.80 – 4.782 = 5.318
(2 sig. figs. After decimal) = 5.32
Multiplying/ Dividing and Significant
Figures
 The rule
– When multiplying or dividing, check out how
many significant figures (all of them) each
number has. Which one has the least amount?
That’s how many significant figures your answer
can have.
Examples
 3.9 × 6.05 × 420 = 9909.9
(2 sig. figs total) = 9900
= 9.9 × 103
 14.2 ÷ 5 = 2.82
(1 sig. fig total) = 3
Scientific Notation
 Do you know this number?
– 300 000 000 m/s
– It’s the speed of light.
 Do you know this number?
– 0.000 000 000 752kg
– It’s the mass of a dust particle.
Scientific Notation
 Instead of counting zeroes and getting confused,
we use scientific notation to write really big or
small numbers.
– 3.00 × 108 m/s
– 7.53 × 10-10 kg
– The 1st number is the COEFFICIENT- it is always a
number between 1 and 10.
– The 2nd number is the BASE- it is the number 10 raised
to a power, the power being the number of decimal
places moved.
Using a calculator with scientific
notation
 A number written in scientific notation is
NOT a math problem, it is a number in its
own right. We put it into the calculator in a
specific way!
 IF you have a scientific calculator, find the
button that says EE or EXP.
Scientific Calculators
Scientific Calculators
 The EE or EXP button fills in for the × 10 part of
the number written in scientific notation.
 Let’s say you are adding these two numbers
3.21 × 107 + 6.99 × 106 =
This is how you would enter it into your calculator
3.21 EE 7 + 6.99 EE 6 =
And you would get your answer.
3.91 × 107
Scientists generally work in metric units.
Common prefixes used are the following:
Dimensional Analysis
 is a problem-solving method that uses the
fact that any number or expression can be
multiplied by one without changing its value.
It is a useful technique. The only danger is
that you may end up thinking that chemistry
is simply a math problem - which it definitely
is not.
Dimensional Analysis
 Unit factors may be made from any two
terms that describe the same or equivalent
"amounts" of what we are interested in. For
example, we know that
 1 inch = 2.54 centimeters
 We can make two unit factors from this
information:
 Now, we can solve some problems. Set up each
problem by writing down what you need to find
with a question mark. Then set it equal to the
information that you are given. The problem is
solved by multiplying the given data and its units
by the appropriate unit factors so that only the
desired units are present at the end.
 (1) How many centimeters are in 6.00
inches?
 (2) Express 24.0 cm in inches.
 You can also string many unit factors
together.
 (3) How many seconds are in 2.0 years?
Density- What is it?
 Density is the ratio of mass to volume of a
substance.
– It can be used to identify a substance.
– Ex. Water has a density of 1.00 g/mL
– Ex. Gold has a density of 19.30 g/mL
– Ex. Pumice has a density of 0.65 g/mL
Density & Temperature
 Density = mass/ volume
 d = m/V
 Temperature = measure of the average kinetic
energy a substance has
– 3 scales
 Fahrenheit (°F)
 Celsius (°C)
 Kelvin (K)
Temperature Scale Conversions
 From °C to °F
 T°F = 1.8(T°C) + 32°
 There are 3
temperature scales:
 From °F to °C
 T°C = .56(T°F - 32°)
 From °C to K
 T = T + 273
 From K to °C
 T°C = TK - 273
– Fahrenheit (°F)
– Celsius (°C)
– Kelvin (K)