Transcript Significant Figures and working with measurements

Significant Figures
and working with measurements
Science 10
G.Burgess
Feb.2007.
What is a Significant Figure?
 A number that demonstrates the
precision of a measuring tool.
Rules for Measuring significantly
 Write out all digits shown by the
markings on the measuring tool
 Make a guessed digit for the space
between the markings
 If you are using a mm ruler, you guess a
digit for the space between the mm
markings.
Recognizing Significant Digits in
pre-measured numbers
Rules:
 All digits 1-9 are always significant. IE.
The number 234 has two S.F.’s.
The
number 7344.6 has 5 S.F.’s.
 Zeros to the left of non-zero digits are
not significant.
IE. The number 0078 has 2 S.F.’s.
The number 022 has 2 S.F.’s.
Recognizing Significant Digits in
pre-measured numbers
 Zeros to the right of a non-zero digit are
significant only when a DECIMAL is
present. IE. The number 7000 only
has 1 S.F. because
there is not a
decimal in the number.
The
number 70.00 has 4 S.F.’s because
there is a decimal.
 Zeros between non-zero digits are
significant.
IE. The number 807
has 3 S.F.’s.
The number
70.006 has 5 S.F.’s
Rounding numbers
 Round down all digits ending with 4
or less.
 Round up all digits that are 6 or
more.
 If the digit is a 5;
 If the digit before is odd, round up
 If the digit before is even, round down.
Practice Problems
Round the
following to 3 Sig.
Fig.’s
1. 0.9973
2. 0.01955
3. 6.070
4. 809.2
5. 875.54
6. 0.0019754
7. 201.59
8. 29.27
9. 20.52
10. 687.59300
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Answers
1. 0.997
2. 0.0196
3. 6.07
4. 809
5. 876
6. 0.00198
7. 202
8. 29.3
9. 20.5
10.688
Scientific Notation
 The short hand method for writing
very large or very small numbers and
showing numeric significance
 All notation numbers have a non-zero
digit followed by a decimal and other
significant digits.
 IE. 87.99 rounded to 2SF would be 8.8 X
102
 Check out next slide to find out how.
How to convert to
Scientific Notation

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Converting 0.97580 to
sci.notation.
Write first non-zero digit. In this
case it is the digit 9
Put a decimal after the 9
Write out all other digits
Write X 10



Give the 10 an exponent that
represents the number of places
the decimal was moved.
**minus means decimal was
moved to the left
**plus means the decimal was
moved to the right.
Example:
9
9.
9.7580
9.7580 X 10
9.7580 X 10-1
Using Scientific Notation to show
significance
 The only digits that appear in a
sci.notation number are the significant
ones. IE.
 79,954.094 rounded two significant figures
would be;
 80,000
 Using scientific notation the number would be;
 8.0 X 104
Practice Problems

1.
2.
3.
4.
5.
Convert the
following numbers
to scientific
notations having 3
sig figs.
0.000207
98.256
999.999
5467.3
100809.2
Answers
1. 2.07 X
2. 9.82 X
3. 1.00 X
4. 5.47 X
5. 1.00 X
10-4
101
103
103
106
Multiplying and Dividing with
significant figures
 Your answer must be
rounded to the same
number of significant
digits as the number
with the least number
of significant digits.
75 = 2 SF’s
X 1.256 = 4 SF’s
94.200 = 5 SF’s
**Answer must be
rounded to 2 SF’s.
Answer = 94
Practice Problems
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Complete the following
using Sig figs.
6.25 X 0.3 =___
78 X 0.345 =___
2 x 16 = ___
25.03  5.33 = ___
0.09465  0.00356 = ___
1. 2
2. 27
3. 30
4. 4.70
5. 26.6
Adding and Subtracting with
Significant Figures
 Your answer must have
the same number of
place values as the
number with the least.
18.509 = 3 SF after Decimal
+96.5
= 1 SF after Decimal
115.009 = 3 SF after Decimal
**Our answer must have no more than
1 place after the decimal.
Answer is 115.0
Practice Problems

Complete the following
using Sig figs.
1.
13.05 + 6 = ___
2.
120 + 56.5 =___
3.
1209.9 + .1 = ___
4.
0.98 – 0.0567 = ___
5.
0.16458 - .1307 = ___
Answers
1. 19
2. 176
3. 1210.0
4. 0.92
5. 0.0339