Transcript Significant Figures Powerpoint

Chapter 2
Section 3 Using Scientific Measurements
Significant Figures
• Significant figures in a measurement consist of all
the digits known with certainty plus one final digit,
which is somewhat uncertain or is estimated.
• Significant figures are critical when reporting
scientific data because they give the reader an idea
of how well you could actually measure/report your
data.
• We don’t worry about significant figures when using
“exact” numbers, because they are known with
complete certainty.
Reporting Measurements
Using Significant Figures
Rules for deciding the number of significant figures in a
measured quantity:
(1) All nonzero digits are significant:
1.234 g has 4 significant figures
(2) Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures
(3) Leading zeros to the left of the first nonzero digits are not
significant; such zeroes merely indicate the position of the decimal
point:
0.001 oC has only 1 significant figure
(4) Trailing zeroes that are also to the right of a decimal point in a
number are significant:
0.0230 mL has 3 significant figures
(5) When a number ends in zeroes that are not to the right of a
decimal point, the zeroes are not necessarily significant:
190 miles may be 2 or 3 significant figures,
50,600 calories may be 3, 4, or 5 significant figures.
The potential ambiguity in the last rule can be avoided by the
use of standard exponential, or "scientific," notation.
For example, depending on whether the number of significant
figures is 3, 4, or 5, we would write 50,600 calories as:
4
5.06 × 10 calories (3 significant figures)
4
5.060 × 10 calories (4 significant figures), or
4
5.0600 × 10 calories (5 significant figures).
By writing a number in scientific notation, the number of
significant figures is clearly indicated by the number of
numerical figures in the 'digit' term as shown by these
examples.
Significant Figures
•How many significant figures are in each of the following
measurements?
•a. 28.6 g
•b. 3440. cm
•c. 910 m
•d. 0.046 04 L
•e. 0.006 700 0 kg
•f. 3.05 x 104 g
•g. 60.004 mg
Lets try some more. How many significant figures
are there in the following measurements:
•45.0 cm
______
•1200.0 km
______
•.0045 m
______
•1.020 g
______
•6500. m
______
•4.00 L
______
•.0025 km
______
•67.003 g
______
Significant Figures
Addition or Subtraction with Significant Figures
• When adding or subtracting decimals, the answer
must have the same number of digits to the right of
the decimal point as there are in the measurement
having the fewest digits to the right of the decimal
point.
Multiplication or Division with Significant Figures
• For multiplication or division, the answer can have
no more significant figures than are in the
measurement with the fewest number of significant
figures.
Significant Figures
•Sample Problem
•Carry out the following calculations. Express
each answer to the correct number of significant
figures.
•a.
5.44 m + 2.6103 m
•b.
2.4 g/mL  15.82 mL
Let’s try a couple practice problems.
•4503 + 34.90 + 550 = ?
•1.367 - 1.34 = ?
•4.56 x 2.5 = ?
Rounding Off Numbers
In correcting a number to express the proper number
of sig. fig., we often have to drop off unwanted digits.
Rules for rounding off numbers:
If the digit immediately to the right of the last sig.
fig. is more than 5, you round up.
If the digit immediately to the right of the last sig.
fig. is less than 5, you round down.
35.76 in 3 sig. fig. is 35.8
35.74 in 3 sig. fig. is 35.7
If the digit immediately to the right of the last
sig. fig. is equal to 5, you round up if the last
sig. fig. is odd. You round down if the last sig.
fig. is even. You round up if 5 is followed by
nonzero digits, regardless of whether the last
sig. fig. is odd or even.
24.35 in 3 sig. fig. is 24.4 (round up because last
sig. digit is 3, an odd number)
24.25 in 3 sig. fig. is 24.2 (round down because
last sig. digit is 2, an even number)
24.258 in 3 sig. fig. is 24.3 (round up because the
digits 58 means it is past halfway to 24.3)
Math using sig figs
Practice Problems
Addition/Subtraction
•+
34.702 cm
12.3 cm
•
•+
45.0325 g
12.34 g
•
-
190.450 m
100.5
m
5.600 km
- 2.30 km
Multiplication/Division
•34.5 m x 1.2 m =
•1,200 kg x 2.3 kg =
•34.6 m / 4.2 =
•.3400 g / 8.2
Rounding
• 43.48 cm (to 3 sig figs) =
• 12.42 cm (to 3 sig figs) =
• 9.275 g (to 3 sig figs) =
• 20.35 g (to 3 sig figs) =
Try these problems:
72.49 in 3 sig. fig. is ___________
292000 in 2 sig. fig. is ___________
45.52 in 3 sig. fig. is ___________
92,528 in 4 sig. fig. is ___________
120.05 in 4 sig. fig. is ___________
13,052 in 3 sig. fig. is ___________
239.5 in 3 sig. fig. is ___________
2.448 x 104 in 3 sig. fig. is ___________
28.149 in 3 sig. fig. is ___________
32000.000 in 3 sig. fig. is ___________
63500 in 2 sig. fig. is ___________
89999 in 3 sig. fig. is ___________