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 Whats so significant about significant digits ID: 402295
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Slide1
Significant digits
Objectives:
State the purpose of significant digits
State and apply the rules for counting and doing calculations with significant digitsSlide2
One way engineers use significant digits….Slide3Slide4
What's so significant about significant digits?Slide5
Significant digits
Measurements that indicate the precision of the tool used
Important—we want to let other scientists and engineers know how “good” our measurements are!Slide6
3.42 cm
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 digitsSlide7
3900 cm
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 digitsSlide8
3900. cm
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 digitsSlide9
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
.)Slide10
Examples of Sig zeros
Examples
of NON-sig zeros
5,00256
00..300.0050.03
3050,000,000This number has a mix of significant and insignificant zeros:0.00300Slide11
Rules for counting significant digits:
2300
23
00Non-zeros are significant2300 zeros are at the end of a number without a decimal =
insignificant2300 =
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.)Slide12
Counting significant digits:
230.
23
0. Non-zeros = significant230. zero here is at the end of a number WITH
a decimal = significant230. = 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.Slide13
Counting significant digits:
2.300 x
10
-3 BIG IDEA: count the digits of the coefficient only2.300 x 10-3
Non-zeros = significant2.300 x10-3
zeros here are at the end of a number and AFTER a decimal = significant2.300 x 10-3 = 4
s.f.
This means the tool allowed us to measure
.00230
, and we estimated it was exactly at
.00230
0Slide14
Counting significant digits - Practice
0.00400
0.00
400 Non-zeros = significant!0.00400
zeros here are at the beginning of a number = insignificant0.00400 zeros here are at the end of a number and
AFTER a decimal = significant0.00400 = 3 s.f.This means the tool allowed us to measure 0.0040, and we estimated it was exactly at 0.00400.Slide15
Practice
Problems 1-10 on your notesSlide16
Compare numbers – which is more precise and how do you know. Game – cc. add this to
prac
probsGive practical example – ie 2 diff thermoms to meas the same tempSlide17
Practice - Answers
State the number of significant digits.
1) 1234
42) 0.023 23) 890 2
4) 91010 45) 9010.0 5 6) 1090.0010 8
7) 0.00120 38) 3.4 x 104 29) 9.0 x 10-3
2
10
) 9.010 x 10
-2
4Slide18
Calculations:
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 caseAnother day multiplying and dividing USE least number of total sig fig
s as the # of sig figs for your answer.Slide19
Example:
350.83 kg + 400.0 kg
350.83
2decimal places400.0 1 decimal place
Lowest # of decimal places = 1750.83 kgI need to round this to only one decimal place
750.8 kgSlide20
Example:
2.0
x 8000
2.0 2
significant figures8000 1 significant figure
LEAST? = 116,000I need to round this to only one significant digit120,000Slide21
Practice
Problems 11-20 in your notesSlide22
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 10
4
)x (2.0 x 10
1
)
=
6.0
x
10
5
6.0 x 10
5
(
9.000 x 10
-2
)÷ (3.00 x
10
1
) =
3.000
x
10
-3
3
.00
x
10
-3
(
3.0 x 10
4
) - (2.0 x 10
1
) = 2.998
x
10
4
3
.0
x 10
4
Slide23
Exit TicketSlide24Slide25
2300Slide26
Counting significant digits:
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?Slide27
Counting significant digits:
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?Slide28
Counting significant digits:
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?Slide29
Counting significant digits:
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?Slide30
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 = significant23.00 = 4 s.f.
This means the tool allowed us to measure 23.0, and we estimated it was exactly at 23.0.Slide31
Example:
10.75
– 0.411
10.75 2 decimal places0.411 3 decimal places
LEAST? = 210.339I need to round this to only two decimal place!
10.34