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• Includes all the digits that are known, plus one
that is estimated
1. Measuring error = 1/10 of smallest division
i.
ii.
iii.
11.65 cm
What is the following measurement with the proper
number of sig. figs.?
**Measure
from the
bottom of
the
meniscus
40.30 mL
Estimated digit
500
550
555
555.5
P
A
Present vs. Absent
• If the decimal is present find the first non-zero
digit starting from the left, count the digit and
all digits to the right as significant
Ex. 1: 200.0
4 s.f.
Ex. 2: 0.0030
2 s.f.
• If the decimal is absent find the first non-zero
digit starting from the right, count the digit
and all digits to the left as significant
Ex. 1: 2930
3 s.f.
Greater than
or equal to 1
NO
Find the first
nonzero digit,
everything after
is significant
**for zeros use
the “after after”
rule
YES
Is there a
decimal point?
NO
Every nonzero
number is
significant
**for zeros use the
“Oreo cookie” rule
YES
Everything is
significant
“Oreo cookie rule”
• Zeros between nonzero digits are significant
Ex) 50,006 has five significant figures
“After After rule”
• Zeros after a non zero digit and after a decimal
point are significant
Ex) 0.0456000 has six significant figures
1. How many significant figures are in the numbers
below?
i.
ii.
iii.
iv.
23,459
300,004
0.042
35.00000
5 sig figs
6 sig figs
2 sig figs
7 sig figs
A. Determine how many significant figures are
needed
B. Find the counting number— first nonzero
number (starting from the left)
C. Count how many sig. figs. you need
D. Underline the last digit counted
E. Round the underlined digit by:
1. If the digit to the right of the underlined digit
is less than five, the underlined digit stays the
same and everything else becomes a zero
place holder or gets dropped off
2. If the digit to the right of the underlined digit
is more than five, the underlined digit is
increased by one and everything else becomes
zero place holder or gets dropped off
**Five or more add one next door
A. Round each number to the specified number of sig. figs.
i.
ii.
iii.
iv.
3.454 (3 sig. fig.) goes to
125,000 (2 sig. fig.) goes to
7,905 (1 sig. fig.) goes to
0.00369847 (2 sig. fig.) goes
to
v. 629.55 (3 sig. fig.) goes to
3.45
130,000
8,000
0.0037
630. ( decimal
point or use)
Scientific
Notation)
A. All digits in the coefficient are significant
B. The exponent is not significant
1. 2.80 ×106 has 3 significant figures
1.
Give the correct number of significant figures
i. 2.3445 x 10-6
ii. 2.69 x 10
iii. 3.4 x 103
(5)
(3)
(2)
2. Round each number to 3 significant figures
i. 87.073 meters 87.1 meters
ii. 4.3621 x 108
4.36 x 108
iii. 0.01552 meter 0.0155 meters
9010 meters
iv. 9009 meters
-3
-3
1.78
x
10
v. 1.77777 x 10