1 Scientific measurement measurement

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

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

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

5 Let’s use a golf anaolgy

6 Accurate?No Precise?Yes

7 Accurate?Yes Precise?Yes

8 Precise?No Accurate?No

9 Accurate?Yes Precise?We cant say!

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

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?= cm

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 has five sig fig

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 has three sig fig has one sig fig

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 has four sig fig has seven sig fig has five sig fig

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.

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

17 Sig Figs. l g l 4050 g l g l g l g l Next we learn the rules for calculations

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 _  7.9 

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) = SF 3 SF

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

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) = rounded down Calculator answer 3 sf 4sf Check multiple rule (least # of sigfig), then round

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 to four sig figs l to three sig figs l to two sig figs l to one sig fig

23 Practice l l l l 6.0 x x 10 3 l l l l 6.0 x x 10 -3

24 Multiplication and Division l 4.5 / l 4.5 x l x.043 l / 1983 l / 714