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Uncertainty & significant figures. Feb 7, 2013. Accuracy & precision. All measurements have some amount of uncertainties, also called “errors”. The uncertainty is generally one half of the smallest scale division. The uncertainty is the measure of the precision of an instrument.

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Accuracy precision
Accuracy & precision

  • All measurements have some amount of uncertainties, also called “errors”.

  • The uncertainty is generally one half of the smallest scale division.

  • The uncertainty is the measure of the precision of an instrument.

  • A precise measurement has more significant figures than less precise measurements.


Which measurement is precise
Which measurement is precise?

  • 5.3, 5.34, 6.001

  • 3.12, 4.190, 0.00001


Significant figures why need to learn
Significant figures:Why need to learn?

  • Significant figures reflect how accurate and precise a measurement is.

    Eg.

    11s - The time is accurate to the nearest second.

What about 11.0s & 10.97s?



Adding subtracting measurements correct to the least accuracy
Adding/subtracting measurements:correct to the least accuracy

Add the measurements:

  • 3.2 m and 5.16 m

  • 100 m and 2.14 m

    Subtract the 1st measurement from the 2nd one

  • 12.5 kg and 25.47 kg

  • 36.52 m and 4.35 m

Multiplying & dividing …..


Multiplying dividing
Multiplying/dividing

Keep the least significant figures!

32.5 x 1.2 =


What about multiplying a whole number?

It depends!

Eg1. The thickness of a book is 2.1 cm. The total thickness of 3 books is:

3 x 2.1=6.3 cm

Eg2. A student measured a basketball court of WSC. Its length is 28.65 m and width is 23 m

Its area is:

28.65 x 23 = 658.95 sq. m

its area is 660 sq. m (least s. f.)


Adding subtracting measurements with uncertainties
Adding /subtracting measurements with uncertainties

  • Add/subtract the measurements

  • Add the absolute uncertainties.

Q1. Given that a = 20.23 0.05 m, b = 12.02 0.05 m

a. find a+b

b. complete the sentence:

The sum of a and b is between _________ and __________.


Find axb
Find axb.

Multiplying/dividing measurements?

Add relative uncertainties.

  • Convert the absolute uncertainties to relative uncertainties.

  • Add the relative uncertainties.

  • State your result with uncertainties.


axb=243.2 0.6%


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