Transcript Significant Figures - Lincoln Park High School

Bell? /DLO
DLO
Bell ?
 Be able to count and
 What are sig
use significant figures
 Be able to measure
properly
figs…again?
Significant Figures
IDENTIFYING AND WORKING WITH
SIGNIFICANT FIGURES
Significant Figures
 There is a limit to the number of digits a
measurement can have.
 This limit communicates the significance of the
numbers in the measurement.
 For example, 35 meters is not as significant or
precise a measurement as 35.319 meters.
 In the first measurement there is less certainty in the
measurement since it is only accurate to the tens
place, while the second is accurate to the
thousandths place.
What is a significant figure?
 Significant figures are the following:
 Any non-zero number
 Zeroes in some cases but not others
 I’m sure that was really clear so lets look at a few examples.
Number
# of Significant
Figures
Reason
365
3
all numbers are non-zero
303
3
the zero is sandwiched between
two non-zero numbers
300
1
the zeros are just place holders
300.0
4
this is an exact measurement
Tricks for determining significant figures
 Here are some tricks to help you figure out how
many significant figures are in a number.

Look at the number and see if a decimal is present or absent.
365 3.03 300 0.003 3050 3.00 3.0120
Tricks for determining significant figures

365 3.03 300 0.003 3050 3.00 3.0120
3.03
Atlantic
If the decimal is PRESENT
start from the PACIFIC side of
the number and find the first
non-zero number.
That first non-zero number that
you come to and everything to
the right of that number are
significant digits.
Pacific

Tricks for determining significant figures

365 3.03 300 0.003 3050 3.00 3.0120-
365

Atlantic
If the decimal is ABSENT start
from the ATLANTIC side of the
number and find the first nonzero number.
That first non-zero number that
you come to and everything to
the left of that number are
significant digits.
Pacific

Significant Figures in Math
 In most cases you will be working with the same
measurement tool which means you will have the
same number of significant figures.
 Sometimes you will have numbers from two different
tools which could mean two different sets of
significant figures.
 In the last case you will need to make adjustments in
your final answer to account for the significant
figures in your problems.
Significant Figures-Addition & Subtraction
 When adding and subtracting numbers, the answer
cannot have more significant places past the decimal
than the least accurate number.
 Example:
236.51
35.5
300.199
+ 1.62
573.829
becomes
573.8
Significant Figures-Multiplication & Division
 When multiplying and dividing numbers the answer
cannot have more significant digits than the number
with the least significant digits.
 Example:
26.51
x 35.4
938.454
becomes
938
 Count the number of significant figures:
1) 1600
Trailing zeroes count
when there is a decimal
point present
2) 11.0
3) 253
4) .0000890
5) 0.0103

All Nonzero numbers
Trailing zeroes count
count
when there is a decimal
point present
All Zeroes before
nonzero numbers
NEVER Count!
In between Zeroes ALWAYS count
Qz Cont’d
Write the Answer to the following problems USING
CORRECT SIGNIFICANT FIGURES
6) 5.45 + 11.0
Decimal Unrounded=16.45 rounded=16.5
2 #’s after 1 #’s after
7) 14.5678 - 12.001
4 #’s after
Sig Figs U.R=67
rounded=70
1 SF
9) (113.2 x 5) + 11.45
4 SF
rounded=2.567
3 #’s after
8) 2.68 ÷ .04
3 SF
Decimal U.R=2.5668
1 SF
10) 1.92 x 103
3 SF
Sig Figs U.R=577.45 rounded=600
3 SF
Sig Figs Answer=1920
Scientific Notation
Scientific Notation
 In science the numbers can be extremely large or
small and becomes inconvenient to write numbers
with a lot of zeroes.
 For example the value for something is
0.000000000382 which is not only a pain to write
but also difficult to say.
 We use scientific notation to clean it up. Doing so
makes this number 3.82 x 10-10
 How did I do that?
Scientific Notation
 First start with the number and moving the decimal
 If the number is small move the decimal behind the first nonzero number
0.000372 → 3.72
 Now you have to account for the zeroes you replaced by using a
power of 10.
Count how many places you moved the decimal. This is the
exponent for the power of 10.
 If you moved the decimal to the left the exponent is positive, to the
right is negative.
3.72 x 10 -4

Scientific Notation
 First start with the number and moving the decimal
 If the number is large move the decimal behind the last nonzero number
37200 → 3.72
 Now you have to account for the zeroes you replaced by using a
power of 10.
Count how many places you moved the decimal. This is the
exponent for the power of 10.
 If you moved the decimal to the left the exponent is positive, to the
right is negative.
3.72 x 10 4

Using Scientific Notation
 Not only does it make it easier to express numbers
but it also can help you express them with the correct
significant figures.
 Suppose you are asked to express 200, 000 with only
3 significant figures.
 See if you can figure it out using scientific notation.
 Keep in mind that the final number must be written
so that it is greater than 1 and less than 10.