Transcript H-Physics Significant Digits PP

Significant Digits
Ch 1 Notes
Significant Digits
Used to round measured values
when involved in calculations
When in scientific notation, all
numbers on left side of number are
significant
Significant Digits
Nonzero #’s are always significant
349
1639
3 sig figs
4 sig figs
Significant Digits
Leading Zeros are never significant
0.0055
2 sig figs
0.0000000393
3 sig figs
Captive Zeros are always significant
5908
2100004
4 sig figs
7 sig figs
Significant Digits
Trailing Zeros are significant IF
there is a decimal point in the #
800
1 sig fig
2900
2 sig figs
800.0
2900.
4 sig figs
4 sig figs
Operations with Sig Figs
Multiplication/Division rule:
Retain the same number of sig
figs in the answer as the factor
containing the least number of sig
figs.
4.5 x 2 = 9.0
rounds to 9
2000 x 21 = 42000 rounds to 40000
11 x 3 x 212 = 6996 rounds to 7000
Operations with Sig Figs
Addition/Subtraction Rule
leave the answer rounded to the
same precision (same decimal place)
as the least precise number involved
in the operation.
2 + 2.3 = 4.3
rounds to 4
120 + 11 = 131
rounds to 130
1.65 + 3 – 2.90 = 1.75
rounds to 2
Sig Fig Examples
#1:
23.0
4.25
+ 25,620
#2:
2.3 x 10-4
316
Examples Solutions
#1:
23.0
4.75
+ 25,620
25,647.75
rounds to 25,650
#2:
2.3 x 10-4
316
= 7.27 x
rounds to 7.3 x
2sf
3sf
10-7
10-7
Sig Fig Situation #1: Let’s Not But
Say We Did
Don’t worry about rounding combo
problems until all the work in the
calculator is done, but heed the rules
as if you did to find out # of digits
needed in the end:
(3.5 + 2.9454) / 357 = (6.4454)/357
= 0.018054341
Rounding: addition to tenths digit, which
would leave 2 sig figs. 2 sig figs divided
by 3 sig figs leaves 2 in answer: 0.018
Sig Fig Situation #2: Less than
Zero
2000 (1 sig fig) vs. 2001 (4 sig figs)
What if you want 2000 to have 4 sig
figs like 2001?
2.000 x 103 for 4 sig figs
2.00 x 103 for 3 sig figs
2.0 x 103 for 2 sig figs
2 x 103 for 1 sig fig
Sig Figs Situation #3: Exact #’s
Whenever a quantity has no
uncertainty, it does not affect the #
of sig figs in answer if x/÷/+/Ex: four sides of a square…if one
side has a length of 2.0 m, then
4 (exact #) x 2.0 m = 8.0 m (retain
two sig figs cause exact # doesn’t
matter to sig fig rounding
Sig Figs Situation #4: Units!
Units are to be treated in the same
algebraic sense as variables
Units do not affect sig figs but must be
common to add/subtract values
23 g + 32.00 g = 55.00 rounds to 55 g
23 g x 32.00 g = 736.0000 rounds to 740 g2
23 kg + 27 ml cannot be simplified