Transcript Significant digits

Significant digits
Objectives:
• State the purpose of significant digits
• State and apply the rules for counting and doing
calculations with significant digits
One way engineers use significant
digits….
Significant digits
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Measurements that indicate the precision
of the tool used
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Important—we want to let other
scientists and engineers know how
“good” our measurements are!
3.42 cm
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This means:
◦ My tool had markings to the tenths place (I can
COUNT them)
◦ I estimated the hundredths place (the object was
between 3.4 and 3.5 but closer to 3.4)
◦  3 significant digits
3900 cm
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This means:
◦ My tool had markings to the thousands place
(I could COUNT them)
◦ I estimated the hundreds place (the object
was between 3000 and 4000 but much
closer to 4000 )
◦  2 significant digits
3900. cm
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This means:
◦ My tool had markings to the tens place (I
could COUNT them)
◦ I estimated the ones place (the object
appeared to be right at 3900)
◦  4 significant digits
Clues: How to know when a
number is significant
It is a non-zero (1, 2, 3, 4, 5, 6, 7, 8, 9)
 It is a zero at the END of a decimal
AFTER a decimal point (4.500)
 It is a zero between non-zeros (5,005)
 It is a zero at the end of a whole number
AND there is a decimal (50.)
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Examples of Sig
zeros
5,002
5600.
.30
Examples of NONsig zeros
0.005
0.03
30
50,000,000
This number has a mix of significant and
insignificant zeros:
0.00300
Rules for counting significant digits:
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2300
2300Non-zeros are significant
2300 zeros are at the end of a number
without a decimal = insignificant
2300 = 2 s.f.
This means the tool allowed us to
COUNT the thousands place, and
estimate the hundreds place (we
counted to 2000 and we estimated the value
was between 2000 and 3000, but closer to
2000.)
Counting significant digits:
230.
 230. Non-zeros = significant
 230. zero here is at the end of a
number WITH a decimal = significant
 230. = 3 s.f
 This means the tool allowed us to
COUNT to the ones place 230 and we
estimated that the value was exactly at
230.
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Counting significant digits:
2.300 x 10-3
 BIG IDEA: count the digits of the coefficient
only
 2.300 x 10-3  Non-zeros = significant
 2.300 x10-3  zeros here are at the end of a
number and AFTER a decimal = significant
 2.300 x 10-3 = 4 s.f.
 This means the tool allowed us to measure
.00230, and we estimated it was exactly at
.002300
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Counting significant digits - Practice
0.00400
 0.00400  Non-zeros = significant!
 0.00400 zeros here are at the beginning of
a number = insignificant
 0.00400 zeros here are at the end of a
number and AFTER a decimal = significant
 0.00400 = 3 s.f.
 This means the tool allowed us to measure
0.0040, and we estimated it was exactly at
0.00400.
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Practice
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Problems 1-10 on your notes
Compare numbers – which is more
precise and how do you know. Game – cc.
add this to prac probs
 Give practical example – ie 2 diff
thermoms to meas the same temp
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Practice - Answers
State the number of significant digits.
1)
1234  4
2)
0.023  2
3)
890  2
4)
91010  4
5)
9010.0  5
6)
1090.0010  8
7)
0.00120  3
8)
3.4 x 104  2
9)
9.0 x 10-3  2
10) 9.010 x 10-2  4
Calculations:
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Addition and subtraction: USE lowest
number of decimal places as the # of
decimal places for your answer. Just do
add probs in class maybe 1 subt. Prep to
not have add and subt, and have it just in
case
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Another day multiplying and dividing USE
least number of total sig figs as the # of
sig figs for your answer.
Example:
350.83 kg +
400.0 kg
750.83 kg
350.83  2decimal places
400.0  1 decimal place
Lowest # of decimal places
=1
I need to round this to only
one decimal place
750.8 kg
Example:
2.0 x 8000
16,000
2.0  2 significant figures
8000  1 significant figure
LEAST? = 1
I need to round this to only
one significant digit1
20,000
Practice
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Problems 11-20 in your notes
Practice - Answers
5.33 + 6.020 = 11.350  11.35
5.0 x 8 = 40.0  40
81÷ 9.0 = 9.0  9.0
3.456 – 2.455= 1.001 1.001
5.5 – 2.500 =3.000  3.0
7.0 x 200 =1400.0  1000
300. ÷ 10.0 = 3.0  3
(3.0 x 104)x (2.0 x 101) = 6.0 x 105  6.0 x 105
(9.000 x 10-2)÷ (3.00 x 101) = 3.000 x 10-3  3.00
x 10-3
 (3.0 x 104) - (2.0 x 101) = 2.998 x 104  3.0 x
104
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Exit Ticket
2300
Counting significant digits:
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450.0
◦ What do we know about the measurement
made?
◦ How many significant digits are in the
answer?
◦ Is this number more less precise than the
previous answer?
Counting significant digits:
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20
◦ What do we know about the measurement
made?
◦ How many significant digits are in the
answer?
◦ Is this number more less precise than the
previous answer?
Counting significant digits:
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0.000450
◦ What do we know about the measurement
made?
◦ How many significant digits are in the
answer?
◦ Is this number more less precise than the
previous answer?
Counting significant digits:
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3,006
◦ What do we know about the measurement
made?
◦ How many significant digits are in the
answer?
◦ Is this number more less precise than the
previous answer?
Counting significant digits:
23.00
 23.00  Non-zeros = significant!
 23.00  zeros here are at the end of a
number and AFTER a decimal =
significant
 23.00 = 4 s.f.
 This means the tool allowed us to
measure 23.0, and we estimated it was
exactly at 23.0.
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Example:
10.75 – 0.411
10.339
10.75  2 decimal places
0.411 3 decimal places
LEAST? = 2
I need to round this to only
two decimal place!
10.34