Significant Figures
• Every measurement has a limit on its
accuracy based on the properties of the
instrument used.
• we must indicate the precision of the
measurement by using the correct number
of significant figures
• Precision – the consistency of a
measurement, how repeatable it is
Can you name this significant
figure?
Object A, measured with Ruler I should be recorded as ________
but as measured with Ruler II should be recorded as _________
Check your answer with the person next to you
Object B, measured with Ruler I is _______________
Object B, measured with Ruler II is _______________
Check your answer with the person next to you
Which ruler is the most precise?
Which ruler is the least accurate?
What happens if an object is directly on the 3 of the ruler?
What decimal place to record?
what is its smallest division? _________
How should measurements using Ruler IV be recorded (to
how many decimal places)? ________
Check your answer with the person next to you
Rules for SigFigs
• Nonzero digits are ALWAYS significant
• Zeroes are only sometimes significant…
– All final zeroes after a decimal point are significant
– Zeroes between two other significant digits are
always significant
– Zeroes used soley as placeholders are NOT
significant
– Zeroes between a decimal point and a nonzero digit
are NOT significant.
Some examples
0.0860 m
$18,000
1.0030 s
0.000010203 m
$18,000.00
$18,000.
0.10001 cm
• 1. Give the number of sig. fig. and the number of
decimal places in each of the number below.
• a) 72.32
b) 10.002
c) 0.003
d) 0.00170
e) 3,000
f) 3,000.
g) 3,000.00
# of sig. fig.
# of decimal places
a) 72.32
4
2
b) 10.002
5
3
c) 0.003
1
3
d) 0.00170
3
5
e) 3,000
assume 1
0
f) 3,000.
4
0
g) 3,000.00
6
2
• 2. These numbers have ambiguous
zeroes. Remove the ambiguity by
expressing them in scientific notation.
• a) 42000 in 2 sig. fig.
b) 42000 in 3 sig. fig.
c) 42000 in 4 sig. fig.
d) 2100 in 3 sig. fig.
e) 790,000 in 4 sig. fig.
f) 3800 x 10-7 in 3 sig. fig.
Answers
a) 42000 in 2 sig. fig.
4.2 x104
b) 42000 in 3 sig. fig.
4.20 x 104
c) 42000 in 4 sig. fig.
4.200 x 104
d) 2100 in 3 sig. fig.
2.10 x 103
e) 790,000 in 4 sig. fig.
7.900 x 105
f) 3800 x 10-7 in 3 sig.fig.
3.80 x 10-4
• When you perform any arithmetic
operation, it is important to remember
that the result can never be more
precise than the least precise
measurement.
Adding and Subtracting
• To add or subtract measurements, first perform
the operation, then round off the result to
correspond to the least precise value
involved. For example, add these values:
• 24.686 m + 2.343 m + 3.21 m = 30.239 m
3.21m
Least precise measurement? ______
30.24m
Round answer to _______
Multiply and Divide
• After performing the calculation, note the
factor that has the least number of
significant digits. Round the product or
quotient to this number of digits. For
example, multiply
• 3.22 cm by 2.1 cm = 6.762 cm2
6.8 cm2
• corrected to _________
• Divide these two measurements and
report answer with correct number of
significant digits
• 36.5 m divided by 3.414 s = 10.691 m/s
10.7 m/s
corrected to ________
Let’s review…
• Some Practice problems
1) 2804m
2) 2.84km
3)0.029m
4)0.003068m
5) 4.6x105m 6) 4.06x105m
7) 750m
8) 75m
9)75,000 m
10) 75,000. m 11) 75,000.0m 12) 10 cm
Answers
• Some Practice problems
1) 2804m
2) 2.84km
3)0.029m
4)0.003068m
5) 4.6x105m 6) 4.06x105m
7) 750m
8) 75m
9)75,000 m
10) 75,000. m 11) 75,000.0m 12) 10 cm
More practice!
1)
2)
3)
4)
5)
6)
7)
8)
9)
6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = ?
1.6 km + 1.62 m + 1200 cm = ?
8.264 g - 7.8 g = ?
10.4168 m - 6.0 m = ?
12.00 m + 15.001 kg = ?
131 cm x 2.3 cm = ?
5.7621 m x 6.201 m = ?
20.2 cm divided by 7.41 s = ?
40.002 g divided by 13.000005 ml = ?