Transcript Chemistry You Need to Know

Section 1.5—Significant Digits
Section 1.5 A
Counting significant digits
Taking & Using Measurements
 You learned in Section 1.3 how to take careful
measurements
 Most of the time, you will need to complete
calculations with those measurements to
understand your results
1.00 g
3.0 mL
= 0.3333333333333333333 g/mL
If the actual measurements were only
taken to 1 or 2 decimal places…
how can the answer be known
to and infinite number of
decimal places?
It can’t!
Significant Digits
A significant digit is anything that you
measured in the lab—it has physical
meaning
The real purpose of “significant digits” is to
know how many places to record in an
answer from a calculation
But before we can do this, we need to
learn how to count significant digits in a
measurement
Significant Digit Rules
1
All measured numbers are significant-if it is not measured and is instead counted or
known then we say that they have infinite significant figures.
2
All non-zero numbers are significant
3
Middle zeros are always significant
4
Trailing zeros are significant if there’s a
decimal place
5
Leading zeros are never significant
All the fuss about zeros
102.5 g
125.0 mL
Middle zeros are important…we know that’s a zero (as
opposed to being 112.5)…it was measured to be a zero
The convention is that if there are ending zeros with a
decimal place, the zeros were measured and it’s
indicating how precise the measurement was.
125.0 is between 124.9 and 125.1
125 is between 124 and 126
0.0127 m
The leading zeros will dissapear if the units are
changed without affecting the physical meaning or
precision…therefore they are not significant
0.0127 m is the same as 12.7 mm
Sum it up into 2 Rules
The 4 earlier rules can be summed up into 2 general rules
1
If there is no decimal point in the number,
count from the first non-zero number to the
last non-zero number
2
If there is a decimal point (anywhere in the
number), count from the first non-zero
number to the very end
Examples of Summary Rule 1
1
If there is no decimal point in the number,
count from the first non-zero number to the
last non-zero number
Example:
Count the
number of
significant
figures in
each
number
124
20570
200
150
Examples of Summary Rule 1
1
If there is no decimal point in the number,
count from the first non-zero number to the
last non-zero number
Example:
Count the
number of
significant
figures in
each
number
124
3 significant digits
20570
4 significant digits
200
1 significant digit
150
2 significant digits
Examples of Summary Rule 2
2
If there is a decimal point (anywhere in the
number), count from the first non-zero
number to the very end
Example:
Count the
number of
significant
figures in
each
number
0.00240
240.
370.0
0.02020
Examples of Summary Rule 2
2
If there is a decimal point (anywhere in the
number), count from the first non-zero
number to the very end
Example:
Count the
number of
significant
figures in
each
number
0.00240
3 significant digits
240.
3 significant digits
370.0
4 significant digits
0.02020
4 significant digits
Importance of Trailing Zeros
Just because the zero isn’t “significant”
doesn’t mean it’s not important and you
don’t have to write it!
“250 m” is not the same thing as “25 m” just
because the zero isn’t significant
The zero not being significant just tells us that it’s
a broader range…the real value of “250 m” is
between 240 m & 260 m.
“250. m” with the zero being significant tells us
the range is from 249 m to 251 m
Let’s Practice
Example:
Count the
number of
significant
figures in
each
number
1020 m
0.00205 g
100.0 m
10240 mL
10.320 g
Let’s Practice
Example:
Count the
number of
significant
figures in
each
number
1020 m
3 significant digits
0.00205 g
3 significant digits
100.0 m
4 significant digits
10240 mL
4 significant digits
10.320 g
5 significant digits
Section 1.5 B
Calculations with significant digits
Performing Calculations with Sig Digs
When recording a calculated answer, you can only be as
precise as your least precise measurement
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Always complete the calculations first, and
then round at the end!
Addition & Subtraction Example #1
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
15.502 g
+ 1.25 g
16.752 g
This answer assumes the missing digit in the problem is a
zero…but we really don’t have any idea what it is
Addition & Subtraction Example #1
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
15.502 g
+ 1.25 g
3 decimal places
Lowest is “2”
2 decimal places
16.752 g
Answer is
rounded to 2
decimal places
16.75 g
Addition & Subtraction Example #2
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
10.25 mL
- 2.242 mL
8.008 mL
This answer assumes the missing digit in the problem is a
zero…but we really don’t have any idea what it is
Addition & Subtraction Example #2
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
10.25 mL
- 2.242 mL
2 decimal places
Lowest is “2”
3 decimal places
8.008 mL
Answer is
rounded to 2
decimal places
8.01 mL
Multiplication & Division Example #1
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
10.25 g
2.7 mL
= 3.796296296 g/mL
Multiplication & Division Example #1
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
4 significant digits
Lowest is “2”
10.25 g
2.7 mL
= 3.796296296 g/mL
2 significant digits
Answer is
rounded to 2
sig digs
3.8 g/mL
Multiplication & Division Example #2
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
1.704 g/mL
 2.75 mL
4.686 g
Multiplication & Division Example #2
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
1.704 g/mL
 2.75 mL
4 significant dig
Lowest is “3”
3 significant dig
4.686 g
Answer is
rounded to 3
significant digits
4.69 g
Let’s Practice #1
Example:
Compute &
write the
answer with
the correct
number of
sig digs
0.045 g
+ 1.2 g
Let’s Practice #1
Example:
Compute &
write the
answer with
the correct
number of
sig digs
0.045 g
+ 1.2 g
3 decimal places
Lowest is “1”
1 decimal place
1.245 g
Answer is
rounded to 1
decimal place
1.2 g
Addition & Subtraction use number of decimal places!
Let’s Practice #2
Example:
Compute &
write the
answer with
the correct
number of
sig digs
2.5 g/mL
 23.5 mL
Let’s Practice #2
Example:
Compute &
write the
answer with
the correct
number of
sig digs
2.5 g/mL
 23.5 mL
2 significant dig
Lowest is “2”
3 significant dig
58.75 g
Answer is
rounded to 2
significant digits
59 g
Multiplication & Division use number of significant digits!
Let’s Practice #3
Example:
Compute &
write the
answer with
the correct
number of
sig digs
1.000 g
2.34 mL
Let’s Practice #3
Example:
Compute &
write the
answer with
the correct
number of
sig digs
4 significant digits
1.000 g
2.34 mL
Lowest is “3”
= 0.42735 g/mL
3 significant digits
Answer is
rounded to 3
sig digs
0.427 g/mL
Multiplication & Division use number of significant digits!