Transcript How many sig. figs are there?

Significant Figures
and Rounding
So you can stop asking
“How many decimal places
should I write?”
How many sig. figs are there?
1)
2)
3)
4)
5)
6)
7)
Value
4,233
220
0.004
1.005
0.010
330.
2.201
# of sig figs
4
2
1
4
2
3
4
Sci. notation
4.233 x 103
2.2 x 102
4 x 10-3
1.005 x 100
1.0 x 10-2
3.30 x 102
2.201 x 100
Rules to Rounding

Do we really need to cover this?

0 – 4: Round down

6 – 9: Round up


5 and some other non-zero digit(s):
Round up
5 and no other digit: Round the
previous digit to be EVEN (not odd)
Write each of these to have three
(3) sig figs. Round if you must.
1)
2)
3)
4)
5)
6)
7)
8)
Value
4,233
5,220
15.104
2.005
0.010
330.5
2.225
0.05422
1)
2)
3)
4)
5)
6)
7)
8)
Answers
4,230
5,220
15.1
2.00
0.0100
330.
2.22
0.0542
1)
2)
3)
4)
5)
6)
7)
8)
Why not?
4,200
5,220.
15.10
2.01
0.01
330
2.23
0.054
Multiplication

Remember
• (factor1) x (factor2) x (factorn) = product

Answer (product) should have the
same number of sig figs as the least
of the factors.
• Example:
17.04 x 2.2 = 37.488 (from calculator)
(4 sig fig) x (2 sig fig)  answer with 2 sig figs
37.448  37
Multiplication (cont’d)

Answer (product) should have the
same number of sig figs as the least of
the factors.
• Example:
17.04 x 2.20 = 37.488 (from calculator)
(4 sig fig) x (3 sig fig)  answer with 3 sig figs
37.488  37.5
Only do your rounding in the FINAL STEP
or you could create rounding errors.
Division

Remember
• (dividend) ÷ (divisor) = quotient

Answer (quotient) should have the
same number of sig figs as the lesser
of the dividend or divisor.
• Example:
170 ÷ 2.25 = 75.5555 (from calculator)
(2 sig fig) ÷ (3 sig fig)  answer with 2 sig figs
75.5555  76
Division (cont’d)

Answer (quotient) should have the
same number of sig figs as the lesser
of the dividend or divisor.
• Example:
170. ÷ 2.25 = 75.5555 (from calculator)
(3 sig fig) ÷ (3 sig fig)  answer with 3 sig figs
75.5555  75.6
Only do your rounding in the FINAL STEP
or you could create rounding errors.
How many sig figs does
Computations
the answer have?







10 x 2.55
100 x 25
100. x 25
24.00 / 12.0
480 / 4
22.44 / 14.2
(16 / 2) x 9
1
1
2
3
1
3
1
25.5  30
2500  2000
2500  2500
2  2.00
120  100
1.580 28  1.58
72  70
Put these numbers in
standard notation



102.55 + 101.9
100.0 + 91.22
90 + 25.6
Computations
204.45  204.4
191.22  191.2
115.6  120 or
116 (Why?)




102.55 + 101.9
14,400 + 490
22.74 – 14.2
(16 / 2.0) + 9.0
204.45  204.4
14,890  14,900
18.54  18.5
8.0 + 9.0  17.0
So now you can stop asking
“How many decimal places
should I write?”
Quiz Time
Depending on the class’s behavior,
it may be open-note or closed-note.