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Significant Figures. How do you know when to round a number?. There are rules to determine which numbers are significant. Rule #1. All non-zero numbers are significant 284 has ____ sig figs 123,456 has _____ sig figs. 3. 6. Rule #2. Zeroes between non-zero digits are significant

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Significant Figures

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Significant Figures


How do you know when to round a number?

  • There are rules to determine which numbers are significant


Rule #1

  • All non-zero numbers are significant

    284 has ____ sig figs

    123,456 has _____ sig figs

3

6


Rule #2

  • Zeroes between non-zero digits are significant

    2008 has _____ sig figs

    108 has _____ sig figs

    50000000001 has ____ sig figs

4

3

11


Rule #3

  • Trailing zeroes (those at the end) are not significant unless the number contains a decimal point

    90000 has 1 sig fig

    900.00 has 5 sig figs

    120000 has ____ sig figs

    500.00 has ____ sig figs

2

5


How is it possible to measure 900.00?

  • The number of decimal places in a measurement depends on the piece of equipment used

  • Researchers report all digits they are certain of plus one unit they are uncertain of


20.0 mL

28.1 mL


73.1 mL


Rule #4

  • Zeroes to the left of the first non-zero number are not significant…they are only placeholders

    0.00000485 has ____ sig figs

    0.052 has ____ sig figs

3

2


How many sig figs are in the following numbers?

4

  • 0.0004035 ______

  • 100276 ______

  • 2000 ______

  • 150.40 ______

  • 1.980 ______

6

1

5

4


Precision vs. Accuracy

  • Precision: reproducibility or repeatibility

  • Accuracy: degree of closeness to an accepted value


Rules for Addition and Subtraction

  • Your calculated value will have the same number of sig figs to the right of the decimal point as that of the least precise quantity


Which is least precise?

2.34 + + 10.998

Step 1: Determine least precise number

So the answer will have 1 digit beyond the decimal point

4.5


Step 2: Do the math

2.34 + 4.5 + 10.998=

17.838


Step 3: Round to the appropriate number of sig figs

17.838 

17.8

If 5 or greater  round up


Try these…

  • 17.898 – 15.2 =

  • 32 + 19.4 =

  • 11.1 + 14.29 -3.33 =

2.7

51

22.1


Rules for Multiplication and Division

  • The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs


Which has the fewest number of sig figs?

23.1 x 18.79 =

Step 1: determine least precise number

So the answer will have 3 digits


Step 2: do the math

23.1 x 18.79 =

434.049


Step 3: Round to the appropriate number of sig figs

434.049 

434


Try these…

  • 111 5 =

  • 12.57 x 3.2 =

  • 2.2 x 4.59 x 12.39 =

22.2  20

40.

125  130


Combined Problems

First apply addition/subtraction rules and then apply multiplication/division

(4.32 +5.0) x 768 =

7142  7100

9.3


Why are sig figs used?

  • The science teachers at a Baltimore County middle school wished to acquire a steel cube, one cubic centimeter in size to use as a visual aid to teach the metric system. The machine shop they contacted sent them a work order with instructions to draw the cube and specify its dimensions. On the work order, the science supervisor drew a cube and specified each side to be 1.000 cm.


  • When the machine shop received this job request, they contacted the supervisor to double check that each side was to be one centimeter to four significant figures. The science supervisor, not thinking about the "logistics", verified four significant figures. When the finished cube arrived approximately one month later, it appeared to be a work of art. The sides were mirror smooth and the edges razor sharp.


  • When they looked at the "bottom line", they were shocked to see the cost of the cube to be $500! Thinking an error was made in billing, they contacted the machine shop to ask if the bill was really $5.00, and not $500. At this time, the machine shop verified that the cube was to be made to four significant figure specifications.


  • It was explained to the school, that in order to make a cube of such a high degree of certainty, in addition to using an expensive alloy with a low coefficient of expansion, many man hours were needed to make the cube. The cube had to be ground down, and measured with calipers to within a certain tolerance. This process was repeated until three sides of the cube were successfully completed.


  • So, "parts and labor" to prepare the cube cost $500. The science budget for the school was wiped out for the entire year. This school now has a steel cube worth its weight in gold, because it is a very certain cubic centimeter in size.


Exit Slip

  • Using a triple beam balance and a graduated cylinder, a student collected data on a sample of an element:

    Mass of sample = 18.9 g

    Volume of water = 30.0 mL

    Volume of water and sample = 35.0 mL

    Calculate the density of the sample using sig figs.


35.0 mL – 30.0 mL = 5.0 mL

D = m/v

D = 18.9 g / 5.0 mL =3.8 g/mL


Work on your Measurement Packet pages 6, 7, and 8

Announcement: Measurement packet should be completed by the end of this week and will be collected


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