Physics Help needed

[XPFMember]

Assalamoalaikum!
I have a doubt.....for a question ''explain why the readings are precise but not accurate'' ..what's the correct answer...cuz i'm confused with what precision actually is...is it that the repeated readings if close together they r precise...or if it has more no. of decimal places it is a precise reading? plz answerboth of my questions!
JazakAllah Khair!!

 

[hassam]

lets say u hav a set of data for t(s) i.e time. there r six readings.to calculate the precision ;u ll first calculate the mean value.if the deviations from the mean value are very small,then ur data is precise but if deviations are large ur data is not precise.
Now lets examine the link of significant figures NOT decimal place with precision.
the precision increases with the no. of significant figures.to make this point clearer u can take some random values...say 1.2cm,1.21cm,1.212cm ; in these three values no. of significant figures is increasing...to get an idea abt y precision is also increasing,
u do the same thing i.e calculating the mean valueand then calculating the deviations from th mean value and u ll find that the deviation is least with the no 1.212,then comes 1.21 and at last comes the value with least no. of significant figures.

CONCLUSION: PRECISION increases with the no. of significant digits....

NB:to calculate deviations u subtract the no. from the mean value or vice versa depending on which one is the larger of these two...
well this is the best explanation i can think off abt significant digits and precision.......hope u got my point....feel free to ask any question regardin this.....

 

[hassam]

well math angle u might be interested in smthing critical abt significant figures:
Suppose that we are asked to measure the area of a computer disk label using a meter stick as a measuring instrument. Let us assume that the accuracy to which we can measure with this stick is 0.1 cm. If the length of the label is measured to be 5.5 cm, we can claim only that its length lies somewhere between 5.4 cm and 5.6 cm. In this case, we say that the measured value has two significant figures. Likewise, if the label’s width is measured to be 6.4 cm, the actual value lies between 6.3 cm and 6.5 cm. Note that the significant figures include the first estimated digit. Thus we could write the measured values as (5.5 +or- 0.1) cm and (6.4 +or- 0.1) cm.
Now suppose we want to find the area of the label by multiplying the two measured values. If we were to claim the area is (5.5 cm)(6.4 cm)  35.2 cm2, our answer would be unjustifiable because it contains three significant figures, which is greater than the number of significant figures in either of the measured lengths. A good rule of thumb to use in determining the number of significant figures that can be claimed is as follows:

When multiplying several quantities, the number of significant figures in the
final answer is the same as the number of significant figures in the least accurate
of the quantities being multiplied, where “least accurate” means “having the
lowest number of significant figures.” The same rule applies to division.
Applying this rule to the multiplication example above, we see that the answer
for the area can have only two significant figures because our measured lengths
have only two significant figures. Thus, all we can claim is that the area is 35 cm2,
realizing that the value can range between (5.4 cm)(6.3 cm)  34 cm2 and
(5.6 cm)(6.5 cm)  36 cm2

 

[XPFMember]

lets say u hav a set of data for t(s) i.e time. there r six readings.to calculate the precision ;u ll first calculate the mean value.if the deviations from the mean value are very small,then ur data is precise but if deviations are large ur data is not precise.
Now lets examine the link of significant figures NOT decimal place with precision.
the precision increases with the no. of significant figures.to make this point clearer u can take some random values...say 1.2cm,1.21cm,1.212cm ; in these three values no. of significant figures is increasing...to get an idea abt y precision is also increasing,
u do the same thing i.e calculating the mean valueand then calculating the deviations from th mean value and u ll find that the deviation is least with the no 1.212,then comes 1.21 and at last comes the value with least no. of significant figures.

CONCLUSION: PRECISION increases with the no. of significant digits....

NB:to calculate deviations u subtract the no. from the mean value or vice versa depending on which one is the larger of these two...
well this is the best explanation i can think off abt significant digits and precision.......hope u got my point....feel free to ask any question regardin this.....

yup i understood...JazakAllah
but plz do one thing...tell me how will u answer the question i've asked..it's from 2002 i think june...explain why the readings are precise but nt accurate...actually the question states that a student uses a micrometer screw gauge to measure the diameter of wire...but fails to notice the zero error....so then explain why the readings are precise but not accurate?
the question is not exactly this but this is what i remember..
and from ur explanation what i understand is more no. of significant digits mean if repeated the readings will be very close to each other...so what i was confused with is now cleared with that that both explanations actually mean the same but in different words
thanks a lot...JazakAllah Khair!

 

[hassam]

k lets talk abt micrometer question.u told that question said that micrometer had a zero error which is a systematic error meaning that ur value will always be greater or less than the true value by the same value no matter how much care u take....since accuracy is the degree to which a measurement approaches the true value...if u take measurements with more care using this micrometer which has zero error u r only goin to increase precision since dat depends on deviation from the mean values abtained in the data