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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 36 . 7 cm size 12{"36" "." 7" cm"} {} . You could not express this value as 36 . 71 cm size 12{"36" "." "71"" 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 36 . 6 cm size 12{"36" "." 6" cm"} {} and 36 . 7 cm size 12{"36" "." 7" 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 36 . 7 cm size 12{"36" "." 7" cm"} {} has three digits, or significant figures. Significant figures indicate the precision of a measuring tool that was used to measure a value.


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 × 10 3 size 12{6 times "10" rSup { size 8{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 10 3 size 12{"10" rSup { size 8{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

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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 = πr 2 size 12{A=πr rSup { size 8{2} } } {} . Let us see how many significant figures the area has if the radius has only two—say, r = 1 . 2 m size 12{r=1 "." 2" m"} {} . Then,

Questions & Answers

what is wave
Charity Reply
a wave is a distirbance that transmits energy from one place ro another within or without a medium
wave is the transfer of energy from one medium to another without the transfer of particles
wave is a disturbance which transfer energy from one medium to another without causing any permanent displacement by itself
wave is a disturbance or oscillation that travel through space and matter,accompanied by a transfer of energy
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what is harmonic motion
is a restoring force
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.
what is thermodynamics
Williams Reply
what is thermodynamics
thermodynamics is a heat and energy significant physics
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Daniel Reply
yes. Hadrons are the elementary particles that take part in stong, electromagnetic and weak interactions. Infact only Hadrons are involved in Strong interactions and when an anti-particle of any hadron is produced, it would be a hadron-conservations laws. Leptons are involved in weak int and follow
what is physics
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Owk. But am are Art student.
What happens when an aeroplanes window is opened at cruise altitude?
Theophilus Reply
what is the minimum speed for any object to travel in time?
Pankaj Reply
as per theory of relativity, minimum speed will be the speed of light
what is physics
Lote Reply
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.
like Newton's laws , Kepler's laws etc....
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Kofi Reply
it flies
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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
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what happens when a ship moves
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Conwil Reply
If it reduces the magnitude of the velocity, the acceleration sign is the opposite compared to the velocity.
what is accerelation
John Reply
an objects tendency to speed up over time
acceleration is the change in velocity over the change in time it would be written delta-v over delta-t.
the change in velocity V over a period of time T.
Delta means "change in"...not period of
just kidding. it all works mathematically
except doesn't time really only change if the instantaneous speeds vary...?
and I assume we are all talking average acceleration
Hey shiii 😀
the rate of change of velocity is callaed acceleration
a=delta v/delta t
the rate of change in velocity with respect to time is acceleration
nana you r right
what is meant by lost volt
Hardeyyemih Reply
Lost volt. Lol. It is the electrical energy lost due to the nature or the envirommental conditions (temperature and pressure) that affect the cable across which the potential difference is measured.
What is physics?
Bedabyas Reply
physics is brance science concerned with nature and properties of matter and energy
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physics is study of nature and it's law
physics is a branch of science that deals with the study of matter ,properties of matter and energy
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what is a double-slit experiment?Explain.
Daniel Reply
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what is photoelectric effect
Godwin Reply
the emission of electrons in some materials when light of suitable frequency falls on them
The phenomenon that involves the emission of electrons (photoelectrons) when light of appropriate wavelength and frequency is incident on the surface of a metal.
what is regelation
oladipupo Reply
is the process of melting under pressure and freezing when pressure is reduce
poisons ratio is which chapter
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Daniel Reply
And also from J/s to MeV?I don't quite understand what is in the book,particle physics just in case.
how many significant figures does this number has 4760.2540
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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