Am I Significant?

1
Am I Significant?

• Working with Numbers

2
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
3
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.
4
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.
5
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.
6
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.
7
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?
8
Significant Digits (Cont.)
9
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

10
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/Subtractio
  n and Multiplication/Division

11
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

12
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.
13
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)

14
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

15
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