Name:______Date:______
Physics 11 - Chapter 1 & 2What is physics and Mathematical tools
Lesson #2 Significant Figures
Physics involves collecting data. This involves measuring, and every measuring apparatus has a limit to how precise we can make a measurement. Because of this, the digits in our calculations that we know with certainty are also limited.
Given a measurement, not all numbers are “significant” (should be taken as accurate). When using several measurements to calculate something, it’s important to know what’s important in the end.
RULES FOR ‘SIG FIGS’
1.Any non-zero number counts
4563 sig figs
0.97234 sig figs
2.Zeros to the left of a decimal count.
690.3 sig figs
6902 sig figs no decimal
3.Zeros to the right of a decimal are tricky. If there are numbers to the left of a zero, they count, otherwise ignore them…
67.00 4 sig figs
67.00016 sig figs
0.000352 sig figs
0.003053 sig figs
0.0089004 sig figs
Significant Digits (sig figs):The valid digits in a measurement.
7→1 sig fig
5.2→2 sig figs
0.2→1 sig fig
0.23→2 sig figs
0.008→1 sig fig
0.0080→2 sig figs
186,000→???
(As is, there are 3. But scientific notation will tell us.)
1.86×105→
1.86000×105→
1.860×105→
Non-zeros are always significant.
E.g.
- All final zeros after the decimal point are significant.
- Zeros between two sig figs are significant.
- Zeros as placeholders are NOT.
Rules for + and- : How to add (subtract)
The answer must have the same number of digits after the decimal as the measurement with the least number of digits after the decimal point.
Use the least accurate measurement (by decimal place) in your final answer.
E.g.
Since 7.34m is the least accurate measurement, with two decimal places.
Rules for and : How to multiply (divide)
The answer must have the same number of significant figures as the measurement with the least number of significant figures.
Use the measurement with the fewest sig figs in your final answer.
E.g.
Since 6.1min has the fewest sig figs (two).Any digit (1 - 9) is a significant digit. ex:
Zeros may or may not be significant.
Zeros at the beginning of a quantity are not significant. ex:
Zeros that are between significant digits are significant. ex:
Zeros at the end of a quantity may or may not be significant. ex:
1. How many significant figures are in the following numbers?
a) 425b) 1.2
c) 25.2d) 6.3706
e) 8.11002f) 2500
g) 450,000h) 5080.
i) 0.00897j) 0.1000
k) 7.01 x 103l) 7.00 x 10-4
m) 0.0089700
2. Compute the following - use significant figures.
a) 6.3 + 10.764 + 4.56b) 67.98 + 8 + 43.2
Where do you round off?
RULE #1Never round off until ALL your calculations are finished.
RULE #2Round off to the smallest number of significant digits represented.
c) 56 x 3.21d) 3.72 2.1
RULE #1Use all known digits in the calculation.
RULE #2Round off to the last decimal place that both numbers have in common.
Unit Conversion:
Ex. 1) Convert the following distances to meters:
a) 1.1 cmb) 76.2 pmc) 0.123 Mm
Scientific Notation:
Rewrite the following in scientific notation:
Ex. 1) The Earth weighs 5,980,000,000,000,000,000,000,000 kg.
Ex. 2) One electron has a charge of 0.00000000000000000016 Coulombs.
Ex. 3)
What is the difference between $600 and $599.87 ?
One is more precise than the other. Scientifically, we say that one has more significant (relevant) digits than the other.
$600 has
$599.87 has
Assignments: page 18 #6page 24 #12, 13page 25 # 15 page 26 #16, 17