Download Significant Figures

Significant Figures
1. All non-zero digits are significant
(2.45 has 3 SF)
2. Zeros between (sandwiched)nonzero digits are significant
(303 has 3 SF)
3. Zeros to the left of all non-zero
digits are NEVER significant
(0.000025 has 2 SF and
0.0000125 has 3 SF)
4. Zeros to the right of all non-zero
digits are only significant if they
are also to the right of the decimal
(250 has 2 SF and 250.00 has 5 SF)
5. Counting numbers have infinite
significant figures
(21 students has infinite SF)
6. Exactly defined quantities have
infinite significant figures
(100 cm = 1 m -both terms have
infinite SF)
Practice
•
•
•
•
0.00400
1000
681.000
404.0040
•
•
•
•
3 SF
1 SF
6 SF
7 SF
Adding and Subtracting
with Significant Figures
The answer should have no more
decimal places than the number in the
problem with the least decimal places.
10.21 cm
+ 5.3 cm
15.51 cm =
15.5 cm
Practice
721.493 m
- 508.2 m
213.293 m
7.516 g
+ 2.1 g
9.616 g
0.00307 ml
+ 0.406
ml
0.40907 ml
Multiplying and Dividing
The answer must be rounded to the
same number of significant figures as
the number in the problem with the
least significant figures.
7.83 kg
x 2.1 kg
16.443 kg = 16 kg
27.634 g
12.4 cm3
= 2.228548387 g /cm3
= 2.23 g/ cm3
Practice
(73814.69 m) (21.4 m) =
1579634.366 m2 =
1580000 m2 =
1.58 x 106 m2
(691 g / 0.0004000cm3)
= 1727500 g / cm3
= 1730000 g / cm3
= 1.73 x 106 g / cm3
Rounding
• Select the place you want to round to:
26.3495
• Look at the place after the one you want
to round to:
26.3495
• If < 5
round down
• If ≥ 5
round up
26.35
Practice
• 705.3998
to
4SF
• 0.00638114 to 3SF
• 6.037 x 10-8 to 3SF
• 7831
to
2SF
705.4
(7.054 x 102)
0.00638
(6.38 x 10-3)
6.04 x 10-8
7800
(7.8 x 103)