Transcript 2.4 Significant Figures in Measurement

2.4 Significant Figures in
Measurement

The significant figures in a measurement
include all the digits that are known precisely
plus one last digit that is estimated.

Example: With a thermometer that has 1° intervals,
you may determine that the temperature is between
24°C and 25°C and estimate it to be 24.3°C.
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
You know the first two digits (2 and 4) with certainty, and
the third digit (3) is a “best guest”
By estimating the last digit, you get additional
information
Rules
1. Every nonzero digit in a recorded measurement is
significant.
- Example: 24.7 m, 0.743 m, and 714 m all have three sig.
figs.
2. Zeros appearing between nonzero digits are significant.
- Example: 7003 m, 40.79 m, and 1.503 m all have 4 sig.
figs.
Rules
3. Zeros appearing in front of all nonzero digits are not
significant; they act as placeholders and cannot
arbitrarily be dropped (you can get rid of them by
writing the number in scientific notation).
- Example: 0.0071 m has two sig. figs. And can be
written as 7.1 x 10-3
4. Zeros at the end of the number and to the right
of a decimal point are always significant.
- Example: 43.00 m, 1.010 m, and 9.000 all have
4 sig. figs.
Rules
5. Zeros at the end of a measurement and to the
left of the decimal point are not significant
unless they are measured values (then they
are significant). Numbers can be written in
scientific notation to remove ambiguity.
- Example: 7000 m has 1 sig. fig.; if those zeros
were measured it could be written as 7.000 x 103
Rules
6. Measurements have an unlimited number of
significant figures when they are counted or
if they are exactly defined quantities.
- Example: 23 people or 60 minutes = 1 hour
* You must recognize exact values to round of
answers correctly in calculations involving
measurements.
Significant Figures – Example 1

How many significant figures are in each of the
following measurements?
a. 123 m 3 (rule 1)
b. 0.123 cm 3 (rule 3)
c. 40506 mm 5 (rule 2)
d. 9.8000 x 104 m 5 (rules 4 and 5)
e. 4.5600 m 5 (rule 4)
f. 22 meter sticks Unlimited (rule 6)
g. 0.07080 m 4 (rules 2, 3, and 4)
h. 98000 m 2 (rule 5)
2.4 Concept Practice
7. Write each measurement in scientific notation
and determine the number of significant figures
in each.
a. 0.05730 m 5.730 x 10-2 m, 4
b. 8765 dm 8.765 x 103 dm, 4
c. 0.00073 mm 7.3 x 10-4 mm, 2
d. 12 basketball players 1.2 x 101 BB players, unlimited
e. 0.010 km 1.0 x 10-2 km, 2
f. 507 thumbtacks 5.07 x 102 thumbtacks, unlimited
Significant Figures in Calculations

The number of significant figures in a
measurement refers to the precision of a
measurement; an answer cannot be more
precise than the least precise measurement
from which it was calculated.

Example: The area of a room that measures 7.7 m (2
sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be
41.58 m2 (4 sig. figs.) – you must round the answer to
42 m2
Rounding – The Rule of 5

If the digit to the right of the last sig. fig is less
than 5, all the digits after the last sig. fig. are
dropped.

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Example: 56.212 m rounds to 56.21 m (for 4 sig. figs.)
If the digit to the right is 5 or greater, the value of
the last sig. fig. is increased by 1.

Example: 56.216 m rounds to 56.22 m (for 4 sig. figs.)
Rounding – Example 2
Addition and Subtraction

The answer to an addition or subtraction
problem should be rounded to have the
same number of decimal places as the
measurement with the least number of
decimal places.
Multiplication and Division

In calculations involving multiplication and
division, the answer is rounded off to the
number of significant figures in the least precise
term (least number of sig. figs.) in the
calculations