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1 Scientific measurement measurement

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2 Types of measurement l Quantitative- use numbers to describe l Qualitative- use description without numbers l 4 feet l extra large l Hot l 100ºF

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3 How good are the measurements? l Scientists use two words to describe how good the measurements are l Accuracy- how close the measurement is to the actual value l Precision- how well can the measurement be repeated

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4 Differences l Accuracy can be true of an individual measurement or the average of several l Precision requires several measurements before anything can be said about it l examples

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5 Let’s use a golf anaolgy

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6 Accurate?No Precise?Yes

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7 Accurate?Yes Precise?Yes

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8 Precise?No Accurate?No

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9 Accurate?Yes Precise?We cant say!

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10 1. Significant Figures l Indicate precision of a measurement. l Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

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11 2. NON-ZEROs - significant All NON-Zeros are SIGNIFICANT –1, 2, 3, 4, 5, 6, 7, 8, & 9 –There are ____Sig figs in the measurement below? Answer?= 3 2.35 cm

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12 Rules for determining which ZEROs are significant 3. “SANDWICHED” zeros - significant –Zeros between other nonzero(1,2,3…) digits are significant 50.3 has three sig fig 3.0025 has five sig fig

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13 Rules for determining which ZEROs are significant 4. “BEGINNING” Zeros – not significant –Zeros in front of the 1 st nonzero digit are NOT significant 0.892 has three sig fig 0.0008 has one sig fig

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14 Rules for determining which ZEROs are significant 5. ENDING zeros – significant or not significant? – Ending zeros in a number without a decimal - not significant 1000 has one sig fig –Ending zeros in a number with a decimal - significant 57.00 has four sig fig 2.000000 has seven sig fig 56700. has five sig fig

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15 Sig Figs l Only measurements have sig figs. l Counted numbers are exact l A dozen is exactly 12 l A a piece of paper is measured 11 inches tall. l Being able to locate, and count significant figures is an important skill.

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16 Sig figs. How many sig figs in the following measurements? l 458 g l 4085 g l 4850 g l 0.0485 g l 0.004085 g l 40.004085 g

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17 Sig Figs. l 405.0 g l 4050 g l 0.450 g l 4050.05 g l 0.0500060 g l Next we learn the rules for calculations

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18 6. Add/Subtract – –The final answer should be rounded to have the same number of decimal places as the measurement with the smallest number of decimal places. 3.75 + 4.1_ 7.85 224 + 130 354 7.9 350 3.75 + 4.1 7.85 224 + 130 354

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19 6. Multiply/Divide – –The final answer has the same number of significant figures as the measurement having the least number of sig figures. (13.91)(23.3) = 324.103 324 4 SF 3 SF

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20 7.Rounding? –Always reduce to significance by Rounding when you’ve finished and reached the end of the whole problem. 213.67 - 98 = 115.67 116 round up Calculator answer No decimal places Check addition Rule (least # of decimal places), then round no decimal places 2 decimal places

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21 7.Rounding? –Always reduce to significance by Rounding when you’ve finished and reached the end of the whole problem. 7.32(8.189) = 59.94348 59.9 rounded down Calculator answer 3 sf 4sf Check multiple rule (least # of sigfig), then round

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22 Rounding rules l look at the number behind the one you’re rounding. l If it is 0 to 4 don’t change it l If it is 5 to 9 make it one bigger l round 45.462 to four sig figs l to three sig figs l to two sig figs l to one sig fig

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23 Practice l 4.8 + 6.8765 l 520 + 94.98 l 0.0045 + 2.113 l 6.0 x 10 2 - 3.8 x 10 3 l 5.4 - 3.28 l 6.7 -.542 l 500 -126 l 6.0 x 10 -2 - 3.8 x 10 -3

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24 Multiplication and Division l 4.5 / 6.245 l 4.5 x 6.245 l 9.8764 x.043 l 3.876 / 1983 l 16547 / 714

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