Download Significant Digits

Chapter 1 - Chemistry I
Working with Numbers
Significant Digits
In science numbers are not just numbers they are measurements,
and as we have already discovered ALL measurements have
some degree of uncertainty inherently in them.
Because of this, when we combine certain measurements we
must have the ability to reflect are uncertainty in our final
results.
Scientists’ Answer: SIGNIFICANT DIGITS
Significant Digits (Cont.)
Significant Digits are determined in measurements by
following four distinct rules.
Rule 1: ALL non-zero digits are significant. (1-9)
Rule 2: Zeros preceding (coming before) the first non-zero
number are NEVER significant. (Leading Zeros)
Rule 3: Zeros in between non-zero numbers are ALWAYS
significant. (Trapped Zeros)
Rule 4: Trailing zeros (zeros at the end of a number) are
only significant if a decimal is present.
Significant Digits (Cont.)
Rule 1: ALL non-zero digits are significant.
Example:
12.345 has 5 significant digits since all numbers are
non-zero numbers.
Significant Digits (Cont.)
Rule 2: Zeros preceding (coming before) the first non-zero
number are NEVER significant. (Leading) Zeros
Example:
0.0123 has only 3 significant digits. The zeros
preceding the number 1 are just keeping space in the
number.
Significant Digits (Cont.)
Rule 3: Zeros in between non-zero numbers are ALWAYS
significant. (Trapped Zeros)
Example:
10,023 has only 5 significant digits. The zeros
between the numbers 1 and 2 are a part of the
measurement and must be counted.
Significant Digits (Cont.)
Rule 4: Trailing zeros (zeros at the end of a number) are
only significant if a decimal is present.
Example:
100 has only one significant digit since there is no
decimal present in the number.
100. Has three significant digits, however, since there
is a decimal present.
WHY?
Significant Digits (Cont.)
Significant Digits (Cont.)
• How Many Sig. Digs.
Do the following
numbers have?
• 0.00267001 m
• 19.0550 kg
• 3500 V
• 1,809,000 L
• Answers
•
•
•
•
6 significant digits
6 significant digits
2 significant digits
4 significant digits
Significant Digits (Cont.)
• In scientific calculations we must account
for significant digits because of our
uncertainty in measurement.
• We have two separate rules for
Addition/Subtraction and
Multiplication/Division
Significant Digits (Cont.)
• Rule for Addition/Subtraction
• The number of significant digits allowed in our
calculated answer depends on the number with
the largest uncertainty.
• Example:
951.0 g
•
+1407
g
•
+ 23.911 g
•
+ 158.18 g
•
2539.091 g
Significant Digits (Cont.)
•
951.0 g
• +1407
g
• + 23.911 g
• + 158.18 g
• 2539.091 g
•
•
•
•
•
4 sig digs
4 sig digs
5 sig digs
5 sig digs
7 sig digs
The answer is 2540. g with 4 sig digs. We can only
express our answer to the most uncertain measurement
that we have. In this case, the ones spot.
Significant Digits (Cont.)
• Rule for Multiplication/Division
• The measurement with the smallest number
of significant digits determines the number
of significant digits in the answer.
• Example: V = (3.052 m)(2.10 m)(0.75 m)
Significant Digits (Cont.)
• V = (3.052 m) x (2.10 m) x (0.75 m)
•
(4 sig figs)(3 sig figs)(2 sig figs)
• V = 4.8069 m3 (5 sig figs)
• V = 4.8 m3
Significant Digits (Cont.)
• One Last Rule
• Any numbers that are exact, do not affect
the number of significant digits in the final
answer.
• Exact numbers are constants:
• 12 inches/foot; 3.14, 2.54 cm/inch