1.3 Accuracy, precision, and significant figures  (Page 4/12)

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When we express measured values, we can only list as many digits as we initially measured with our measuring tool. For example, if you use a standard ruler to measure the length of a stick, you may measure it to be $\text{36}\text{.}7\phantom{\rule{0.25em}{0ex}}\text{cm}$ . You could not express this value as $\text{36}\text{.}\text{71}\phantom{\rule{0.25em}{0ex}}\text{cm}$ because your measuring tool was not precise enough to measure a hundredth of a centimeter. It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between $\text{36}\text{.}6\phantom{\rule{0.25em}{0ex}}\text{cm}$ and $\text{36}\text{.}7\phantom{\rule{0.25em}{0ex}}\text{cm}$ , and he or she must estimate the value of the last digit. Using the method of significant figures    , the rule is that the last digit written down in a measurement is the first digit with some uncertainty . In order to determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right. For example, the measured value $\text{36}\text{.}7\phantom{\rule{0.25em}{0ex}}\text{cm}$ has three digits, or significant figures. Significant figures indicate the precision of a measuring tool that was used to measure a value.

Zeros

Special consideration is given to zeros when counting significant figures. The zeros in 0.053 are not significant, because they are only placekeepers that locate the decimal point. There are two significant figures in 0.053. The zeros in 10.053 are not placekeepers but are significant—this number has five significant figures. The zeros in 1300 may or may not be significant depending on the style of writing numbers. They could mean the number is known to the last digit, or they could be placekeepers. So 1300 could have two, three, or four significant figures. (To avoid this ambiguity, write 1300 in scientific notation.) Zeros are significant except when they serve only as placekeepers .

Determine the number of significant figures in the following measurements:

1. 0.0009
2. 15,450.0
3. $6×{\text{10}}^{3}$
4. 87.990
5. 30.42

(a) 1; the zeros in this number are placekeepers that indicate the decimal point

(b) 6; here, the zeros indicate that a measurement was made to the 0.1 decimal point, so the zeros are significant

(c) 1; the value ${\text{10}}^{3}$ signifies the decimal place, not the number of measured values

(d) 5; the final zero indicates that a measurement was made to the 0.001 decimal point, so it is significant

(e) 4; any zeros located in between significant figures in a number are also significant

Significant figures in calculations

When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value . There are two different rules, one for multiplication and division and the other for addition and subtraction, as discussed below.

1. For multiplication and division: The result should have the same number of significant figures as the quantity having the least significant figures entering into the calculation . For example, the area of a circle can be calculated from its radius using $A={\mathrm{\pi r}}^{2}$ . Let us see how many significant figures the area has if the radius has only two—say, $r=1\text{.}2\phantom{\rule{0.25em}{0ex}}\text{m}$ . Then,

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Vincent
wave is the transfer of energy from one medium to another without the transfer of particles
ZIFAC
wave is a disturbance which transfer energy from one medium to another without causing any permanent displacement by itself
Joyfulsounds
wave is a disturbance or oscillation that travel through space and matter,accompanied by a transfer of energy
Ridwan
A wave is any disturbances in an elastic medium which carries energy from one point to another through a medium
abdul
what is harmonic motion
Nozyani
is a restoring force
Joyfulsounds
a wave is a disturbance and there are trasfer energy from one medium to another and travel through any space without the trasfer of particles.
Neha
what is thermodynamics
what is thermodynamics
Charity
thermodynamics is a heat and energy significant physics
Neha
Are the antimatters of Hadrons also Hadrons?!Does the same rule apply to Leptons?
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Lalita
what is physics
physic is a pure science that deal with behavior of matter,energy & how it related to other physical properties
Ridwan
Owk. But am are Art student.
Hussaini
What happens when an aeroplanes window is opened at cruise altitude?
what is the minimum speed for any object to travel in time?
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Mr.
what is physics
it is just a branch of science which deals with the reasons behind the daily activities taking place everyday in our lives. it clearly states the reason in the form of laws.
sandhya
?
lkpostpost2000@yahoo
like Newton's laws , Kepler's laws etc....
sandhya
physics is the study of motion or moving things. Usually the moving things are normal items like vars or planets but sometimes it's electricity or heat that moves.
Jake
physics is one of the most significant diciplines of natural science which describe the nature and its matter
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what happens when an aeroplane takes off?
it flies
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the lift generated by the wing overcome the weight of the plane(in Newton)and a net force of upward is created
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Mr.
then due to lower pressure on upper part of wings helps producing an additional lift because air flows from areaof lower to the area of higher pressure
Mr.
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what happens when a ship moves
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What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
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Nicolas
yes
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what is accerelation
an objects tendency to speed up over time
RayRay
acceleration is the change in velocity over the change in time it would be written delta-v over delta-t.
Shii
the change in velocity V over a period of time T.
Matthew
Delta means "change in"...not period of
Shii
just kidding. it all works mathematically
Shii
except doesn't time really only change if the instantaneous speeds vary...?
Shii
and I assume we are all talking average acceleration
Shii
Hey shiii 😀
the rate of change of velocity is callaed acceleration
Amna
a=delta v/delta t
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the rate of change in velocity with respect to time is acceleration
Nana
nana you r right
Indrajit
good
oguji
what is meant by lost volt
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Theophilus
What is physics?
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George
sure
Okpara
yah....
kashif
physics is study of the natural phenomenon on the basis of certain laws and principles. it's like watching a game of chess and trying to understand its rules how it's played.
Ajit
awesome
Okpara
physics is study of nature and it's law
AMRITA
physics is a branch of science that deals with the study of matter ,properties of matter and energy
Lote
Branch of science (study) of matter, motion and energy
Theophilus
what is a double-slit experiment?Explain.
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Luke
double slit experiment was done by YOUNG. And it's to give out monochromatic coherent, if an incoherent wave is passing through it. And then the waves form interference fringes. The screen placed in front of the double slit is preferably a film and then in the middle where "p=0" a brighter color
navid
is formed and then the constructive interferences occur at 0 (which is the brightest band)... then a sequence of bright band (constructive interference) and dark band (destructive interference) happens and the further from the central band the lower the intensity of bright band(constructive interfe
navid
what is photoelectric effect
the emission of electrons in some materials when light of suitable frequency falls on them
Hardeyyemih
The phenomenon that involves the emission of electrons (photoelectrons) when light of appropriate wavelength and frequency is incident on the surface of a metal.
ibrahim
what is regelation
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bawire
poisons ratio is which chapter
STREET_
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Theophilus
how do i convert energy in MeV/c2 to GeV/c2 and vice versa?
And also from J/s to MeV?I don't quite understand what is in the book,particle physics just in case.
Daniel
how many significant figures does this number has 4760.2540
Nozyani