Measuring with Precision Defn Those numbers that result from directly measuring an object It shows the precision of the measurement Units must be included no units no sd The precision of the measurement depends upon the measuring instrument ID: 643970
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Slide1
Significant (Measured) Digits
Measuring with PrecisionSlide2
Defn: Those numbers that result from directly measuring an object. It shows the precision of the measurement.
Units must be included (no units no sd)
The precision of the measurement depends upon the measuring instrumentUse the following PRIORITIZED list to determine the number of sd’s in a measurement, calculation, or conversion
Significant Digits (sd)Slide3
Rule 1: All nonzero digits are significant (they were measured)
Samples
a. 234 m
b. 1678 cm
c. 0.23 g
SD’s and precision
a. 3 sd to the m
b. 4 sd to the cm
c. 2 sd to the cgSlide4
Rule 2: All zeros between nonzero (or significant) digits are significant
Samples
a. 202 mm
b. 1003 cm
c. 0.200105 m
SD’s and precision
a. 3 sd to the mm
b. 4 sd to the cm
c. 6 sd to the
mm
Translation: In between 0s must be measuredSlide5
Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are
NOT
significant unless otherwise indicated.
a. 200 cm
b. 109,000 m
c. 1,000,000 mm
d. 200 cm
e. 200 cm
a. 1 sd to the m
b. 3 sd to the km
c. 1 sd to the km
d. 3 sd to the cme. 2 sd to the dm
Translation: 0s at the end of a whole number are NOT measured unless marked.
(a bar over a zero indicates the last measured zero)Slide6
Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are
NOT
significant.
Samples
a. 0.0032 m
b. 0.01294 g
c. 0.00000002 L
SD’s and precision
a. 2 sd to the .1 mm
b. 4 sd to the .01 mg
c. 1 sd to the .01
m
L
Translation: 0s in front of a number less than 1 are NOT measured.Slide7
Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant
Samples
a. 20.00 g
b. 0.07080 mm
c. 1.0400 cm
d. 45.00
SD’s and precision
a. 4 sd to the cg
b. 4 sd to the .01
m
m
c. 5 sd to the
m
m
d. 0 sd
Translation: 0s at the end of a decimal number are measured.Slide8
Examine the number & go through rules IN ORDER
Rule 1 - underline any nonzero digits
Rule 2 - underline any zeros between theseRule 3 - place an ‘n’ under the zeros at the end of a whole number (after any overlined 0s)
Rule 4 - place an ‘n’ under zeros in front of a number less than one
Rule 5 - underline zeros at the end of a decimal number
Count the number of underlined digits = # sd
How to use this information when converting/evaluating measuresSlide9
Rule: Your calculation (answer) must have the same precision as the LEAST precise original measurement
Find the number of significant digits in each of the starting numbers and note the lowest number of significant digits
ex. 2.40 cm x 3 cm (lowest # of sd is 1)Calculate your answer
Round the answer to the lowest # of sd found in #1
2.40 cm x 3 cm = (7.2 cm
2
) =
7 cm
2
How to use SD rules when multiplying/dividingSlide10
Significant FiguresSlide11
Significant Figures
All measurements are inaccurate
Precision of measuring deviceHuman error
Faulty techniqueSlide12
Significant Figures
Measurements need to convey precision
Must include degree of uncertaintySig Figs tell us Slide13
Significant FiguresSlide14
Significant Figures
Significant figures in a measurement include
all of the digits that are known precisely
plus one last digit that is estimated
.Slide15
Significant Figures
2. Non-zero digits are always significant.
1
0
3
.
23
000
2Slide16
Significant Figures
3. All final zeros after the decimal point are significant.
12.74
0
0.042
0Slide17
Significant Figures
4. Zeros between two other significant digits are always significant.
1
0
.0
2
00
4
6.
000Slide18
Significant Figures
5. Zeros used only for spacing the decimal point are
not significant.
1
00
0.00000
233Slide19
Killing Babies
Always put a 0 in front of a decimal point
0.247
0.0042
.873
Slide20
Significant FiguresSlide21
Significant Figures
1) 400
2) 200.0
3) 0.0001
4) 218
5) 320
6) 0.00530
7) 22 568
8) 4755.50 Slide22
Significant Figures
1) 4.0 x 10
3
2) 1.67 x 10
-8
3) 5 x 10
12
4) 2.00 x 1045) 635.000
6) 22 000
7) 5201
8) 81 Slide23
Significant Figures
6. If you add or subtract, the answer is rounded to the same number of decimal places as the measurement with the least
number of decimal places.Slide24
Significant Figures
7. If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the least precise term used in the calculation (i.e. the number with the fewest sig figs).Slide25
CalculationsSlide26
Calculations