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A = πr 2 = 3 . 1415927 . . . × 1 . 2 m 2 = 4 . 5238934 m 2 size 12{A=πr rSup { size 8{2} } = left (3 "." "1415927" "." "." "." right ) times left (1 "." 2" m" right ) rSup { size 8{2} } =4 "." "5238934"" m" rSup { size 8{2} } } {}

is what you would get using a calculator that has an eight-digit output. But because the radius has only two significant figures, it limits the calculated quantity to two significant figures or

A = 4 . 5 m 2 , size 12{A" = "4 "." 5" m" rSup { size 8{2} } } {}

even though π size 12{π} {} is good to at least eight digits.

2. For addition and subtraction: The answer can contain no more decimal places than the least precise measurement . Suppose that you buy 7.56-kg of potatoes in a grocery store as measured with a scale with precision 0.01 kg. Then you drop off 6.052-kg of potatoes at your laboratory as measured by a scale with precision 0.001 kg. Finally, you go home and add 13.7 kg of potatoes as measured by a bathroom scale with precision 0.1 kg. How many kilograms of potatoes do you now have, and how many significant figures are appropriate in the answer? The mass is found by simple addition and subtraction:

+ 1 7.56 0 kg = 15.2 kg . - 1 6.052 kg = 15.2 kg . + 13.7 00 kg + 15.208 kg = 15.2 kg . alignl { stack { size 12{7 "." "56"`"kg"} {} #size 12{ - 6 "." "052"`"kg"} {} # size 12{ { {+"13" "." 7`"kg"} over {"15" "." "208"`"kg"} } ="15" "." 2`"kg" "." } {}} } {}

Next, we identify the least precise measurement: 13.7 kg. This measurement is expressed to the 0.1 decimal place, so our final answer must also be expressed to the 0.1 decimal place. Thus, the answer is rounded to the tenths place, giving us 15.2 kg.

Significant figures in this text

In this text, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all worked examples. You will note that an answer given to three digits is based on input good to at least three digits, for example. If the input has fewer significant figures, the answer will also have fewer significant figures. Care is also taken that the number of significant figures is reasonable for the situation posed. In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. Finally, if a number is exact , such as the two in the formula for the circumference of a circle, c = r size 12{c=2πr} {} , it does not affect the number of significant figures in a calculation.

Perform the following calculations and express your answer using the correct number of significant digits.

(a) A woman has two bags weighing 13.5 pounds and one bag with a weight of 10.2 pounds. What is the total weight of the bags?

(b) The force F size 12{F} {} on an object is equal to its mass m size 12{m} {} multiplied by its acceleration a size 12{a} {} . If a wagon with mass 55 kg accelerates at a rate of 0 . 0255  m/s 2 size 12{0 "." "0255"" m/s" rSup { size 8{2} } } {} , what is the force on the wagon? (The unit of force is called the newton, and it is expressed with the symbol N.)

(a) 37.2 pounds; Because the number of bags is an exact value, it is not considered in the significant figures.

(b) 1.4 N; Because the value 55 kg has only two significant figures, the final value must also contain two significant figures.

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Phet explorations: estimation

Explore size estimation in one, two, and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.

Estimation

Summary

  • Accuracy of a measured value refers to how close a measurement is to the correct value. The uncertainty in a measurement is an estimate of the amount by which the measurement result may differ from this value.
  • Precision of measured values refers to how close the agreement is between repeated measurements.
  • The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more precise the tool.
  • Significant figures express the precision of a measuring tool.
  • When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.
  • When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value.

Questions & Answers

What is half-life
Godwin Reply
what is fluid
Anthony Reply
anything that flows is Liquid.
prakash
a substance that has no specific shape
Saleemulhaq
How submarines floats one water the same time sink in water
Courage Reply
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
Arif
define electromagnetic radiation
Anthony
what is work
Ojo Reply
Force times distance
Karanja
product of force and distance...
Arif
Is physics a natural science?
Adebisi Reply
what is the difference between a jet engine and a rocket engine.
Samuel Reply
explain the relationship between momentum and force
Joseph Reply
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
Karanja
How to find Squirrel frontal area from it's surface area?
Pooja Reply
how do we arrange the electronic configuration of elements
Muhammed Reply
hi guys i am an elementary student
benedict Reply
hi
Dancan
hello
adolphus
are you an elementary student too?
benedict
no bro
adolphus
yes
Che
hi
Miranwa
yes
Miranwa
welcome
Miranwa
what is the four equation of motion
Miranwa
what is strain?
SAMUEL
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
ABHIJIT
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
adeleke
How is it possible for one to drink a cold drink from a straw?
Karanja Reply
most possible as it is for you to drink your wine from your straw
Selina
state the law of conservation of energy
Sushma Reply
energy can neither be destroy or created,but can be change from one form to another
dare
yeah
Toheeb
it can neither be created nor destroyed
Toheeb
its so sample question dude
Muhsin
what is the difference between a principle and a law?
Mary Reply
where are from you wendy .?
ghulam
philippines
Mary
why?
Mary
you are beautiful
ghulam
are you physics student
ghulam
laws are ment to be broken
Ge
hehe ghulam where r u from?
Muhsin
yes
dare
principle are meant to be followed
dare
south Africa
dare
here Nigeria
Toheeb
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Ayoka
Rules are meant to be broken while principals to be followed
Karanja
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
tathir
what is momentum?
prakash Reply
is the mass times velocity of an object
True
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
Usman
momentum is the product of the mass of a body of its velocity
Ugbesia
what about kg it is changing or not
vijay Reply
no mass is the quantity or amount of body so it remains constant everywhere
Ahsan
yes
Siyanbola
remains constant
taha
mass of an object is always constant. and that is universally applied.
Shii
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
Saheed
what is hookes law
Joshua
mass of an object does not change
SAMUEL
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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