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Significant (Measured) Digits Significant (Measured) Digits

Significant (Measured) Digits - PowerPoint Presentation

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Significant (Measured) Digits - PPT Presentation

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

figures significant zeros number significant figures number zeros digits decimal rule precision measured 000 nonzero measurement point answer

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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