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Significant Figures
•
Significant figures are used to determine the ______________
precision
of a
measurement. (It is a way of indicating how __________
precise a
measurement is.)
*Example: A scale may read a person’s weight as 135 lbs. Another
scale may read the person’s weight as 135.13 lbs. The ___________
second
more significant figures in the
scale is more precise. It also has ______
measurement.
•
•
•
Whenever you are measuring a value, (such as the length of an object
with a ruler), it must be recorded with the correct number of sig.
figs.
ALL the numbers of the measurement known for sure.
Record ______
Record one last digit for the measurement that is estimated. (This
reading in between the
means that you will be ________________________________
__________
marks of the device and _____________
estimating what the next
number is.)
Significant Figures
•
Practice Problems: What is the length recorded to the correct
number of significant figures?
length = ________cm
11.65
(cm) 10
20
30
40
length = ________cm
58
50
60
70
80
90
100
Rules for Counting Significant Figures in a Measurement
•
When you are given a measurement, you will need to be aware of how
many sig. figs. the value contains.
Here is how you count the number of sig. figs. in a given measurement:
#1 (Non-Zero Rule): All digits 1-9 are significant.
3
*Examples: 2.35 g =_____S.F.
2 S.F.
2200 g = _____
#2 (Straddle Rule): Zeros between two sig. figs. are significant.
*Examples: 205 m =_____S.F.
3
80.04 m =_____S.F.
4
5
7070700 cm =_____S.F.
#3 (Righty-Righty Rule): Zeros to the right of a decimal point AND
anywhere to the right of a sig. fig. are significant.
3
3
*Examples: 2.30 sec. =_____S.F.
20.0 sec. =_____S.F.
4
0.003060 km =_____S.F.
Rules for Counting Significant Figures in a Measurement
#4 (Bar Rule): Any zeros that have a bar placed over them are sig.
(This will only be used for zeros that are not already significant
because of Rules 2 & 3.)
4
*Examples: 3,000,000 m/s =_____S.F.
2
20 lbs =____S.F.
#5 (Counting Rule or Exact #’s): Any time the measurement is
determined by simply counting the number of objects, the value has
an infinite number of sig. figs. (This also includes any conversion
factor known exactly without it being rounded off for ease of use!)
*Examples: 15 students =_____S.F.
∞
29 pencils = ____S.F.
∞
∞
∞
7 days/week =____S.F.
60 sec/min =____S.F.
∞ S.F.
1 inch = exactly 2.54 cm...The measurement “2.54 cm” has ____
•
Scientific Notation
Scientific notation is a way of representing really large or small
numbers using powers of 10.
*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles
0.000 000 042 mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
(1) Write down all the sig. figs.
(2) Put the decimal point between the first and second digit.
(3) Write “x 10”
(4) Count how many places the decimal point has moved from its
original location. This will be the exponent...either + or −.
+ and if the
(5) If the original # was greater than 1, the exponent is (__),
original # was less than 1, the exponent is (__)....(In
−
other words, large
numbers have (__)
+ exponents, and small numbers have (__)
−
exponents.
Scientific Notation
•
Practice Problems: Write the following measurements in scientific
notation or back to their expanded form.
477,000,000 miles = _______________miles
4.77 x 108
0.000 910 m = _________________
m
9.10 x 10−4
−
9
6,300,000,000
6.30 x 10 miles = ___________________ miles
0.00000388
3.88 x 10−6 kg = __________________
kg
Calculations Using Sig. Figs.
•
When adding or subtracting measurements, all answers are to be
rounded off to the least # of ___________
found in
decimal __________
places
the original measurements.
Example:
+
≈ 157.17
•
(only keep 2 decimal places)
When multiplying or dividing measurements, all answers are to be
significant_________
figures found in the
rounded off to the least # of _________
original measurements.
Practice Problems:
(only keep 1
decimal place)
4.7 cm
2.83 cm + 4.009 cm − 2.1 cm = 4.739 cm ≈_____
98 m2
36.4 m x 2.7 m = 98.28 m2 ≈ _____
(only keep 2 sig. figs)
5.9 g/mL
0.52 g ÷ 0.00888 mL = 5.855855 g/mL ≈ ____
(only keep 2
sig. figs)