<< Chapter < Page Chapter >> Page >

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.

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 × 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

Got questions? Get instant answers now!

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

2 how heat loss is prevented in a vacuum flask
Abdullah Reply
what is science
Helen
logical reasoning for a particular phenomenon.
Ajay
I don't know anything about it 😔. I'm sorry, please forgive 😔
Adarsh
due to non in contact mean no conduction and no convection bec of non conducting base and walls and also their is a grape between the layer like to take the example of thermo flask
Abdul
dimensions v²=u²+2at
Lagben Reply
what if time is not given in finding the average velocity?
Alan Reply
the magnetic circuit of a certain of the flux paths in each of the long and short sides being 25cm and 20cm reprectielectrove. there is an air gap of 2mm long in one the long sides if a flux density of 0.8weber/m is to produce in the magnet of 1500 turns..
Daniel Reply
How do you calculate precision
Sacky Reply
what module is that?
Fillemon
Chemisty 1A?
Fillemon
No it has something to do with measurements bro... What we did today in class
Sacky
Tah bra honestly I didn't understand a thing in that class..when re your Tutorials?
Fillemon
Friday bro... But the topics we did are in this app... Just try to master them quickly before the test dates... Are you done with the Maths sheet
Sacky
I eat ass
Anderson
I'll work on the maths sheet tomorrow bra @Sacky Malyenge but I'll try mastering them
Fillemon
I'll eat your mom's ass with a side of tendies
Anderson
@Fillemon Nanwaapo
Anderson
lol, hush
Emi
There are very large numbers of charged particles in most objects. Why, then, don’t most objects exhibit static electricity?
Bilkisu Reply
Because there's an equal number of negative and positive charges... objects are neutral in nature
NELSON
when a ball rolls on a smooth level ground,the motion of its centre is?
Mary Reply
what is electro magnetic field?
Mary
electromagnetic field is a special type of field been produced by electric charges..!!! like the word electro from Electricity and the word magnetic from Magnetism.. so it is more of a join field..!!!
NELSON
Electromagnetic field is caused by moving electric charge
Muhammad
when a ball rolls on a smooth level ground,the motion of its centre is?
Mumeh
what's the relationship btw displacement and position
Declan Reply
displacement is the change of position 8======✊=D 💦💦
Anderson
what is the meaning of elasticity
Pele Reply
is the ability of a material to or any object to expand to a limit point
king
this is about kinematics you bonk
Emi
what does emf/R mean
Eze Reply
What is work
Wisdom Reply
work is the product of force and perpendicular distance
DAVID
Pls explain simple harmonic motion
Olaiya Reply
Any to and from motion of a fluid or any elastic object
Sacky
a current of 5.5mA is flowing through a 3.3k resistor.compute th p.d developed across the resistor
Clifford Reply
A p.d of 24 volts exist across a 15 OHM'S resistor.calculate the current flowing the resistor
Clifford
a current of 5.5mA is flowing through a 3.3kOHM'S resistor.compute th p.d developed across the resistor
Clifford
solve it please
Festus
the so unit power is the watt(w)/joul/second (w1)/s
Jibo Reply
Really
Lawal
what is time
Jibo Reply
a measure of the duration of an event
Raymond
density
Masente
Practice Key Terms 6

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask