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By the end of this section, you will be able to:
  • Define accuracy and precision
  • Distinguish exact and uncertain numbers
  • Correctly represent uncertainty in quantities using significant figures
  • Apply proper rounding rules to computed quantities

Counting is the only type of measurement that is free from uncertainty, provided the number of objects being counted does not change while the counting process is underway. The result of such a counting measurement is an example of an exact number    . If we count eggs in a carton, we know exactly how many eggs the carton contains. The numbers of defined quantities are also exact. By definition, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilogram. Quantities derived from measurements other than counting, however, are uncertain to varying extents due to practical limitations of the measurement process used.

Significant figures in measurement

The numbers of measured quantities, unlike defined or directly counted quantities, are not exact. To measure the volume of liquid in a graduated cylinder, you should make a reading at the bottom of the meniscus, the lowest point on the curved surface of the liquid.

This diagram shows a 25 milliliter graduated cylinder filled with about 20.8 milliliters of fluid. The diagram zooms in on the meniscus, which is the curved surface of the water that is visible when the graduated cylinder is viewed from the side. You make the reading at the lowest point of the curve of the meniscus.
To measure the volume of liquid in this graduated cylinder, you must mentally subdivide the distance between the 21 and 22 mL marks into tenths of a milliliter, and then make a reading (estimate) at the bottom of the meniscus.

Refer to the illustration in [link] . The bottom of the meniscus in this case clearly lies between the 21 and 22 markings, meaning the liquid volume is certainly greater than 21 mL but less than 22 mL. The meniscus appears to be a bit closer to the 22-mL mark than to the 21-mL mark, and so a reasonable estimate of the liquid’s volume would be 21.6 mL. In the number 21.6, then, the digits 2 and 1 are certain, but the 6 is an estimate. Some people might estimate the meniscus position to be equally distant from each of the markings and estimate the tenth-place digit as 5, while others may think it to be even closer to the 22-mL mark and estimate this digit to be 7. Note that it would be pointless to attempt to estimate a digit for the hundredths place, given that the tenths-place digit is uncertain. In general, numerical scales such as the one on this graduated cylinder will permit measurements to one-tenth of the smallest scale division. The scale in this case has 1-mL divisions, and so volumes may be measured to the nearest 0.1 mL.

This concept holds true for all measurements, even if you do not actively make an estimate. If you place a quarter on a standard electronic balance, you may obtain a reading of 6.72 g. The digits 6 and 7 are certain, and the 2 indicates that the mass of the quarter is likely between 6.71 and 6.73 grams. The quarter weighs about 6.72 grams, with a nominal uncertainty in the measurement of ± 0.01 gram. If we weigh the quarter on a more sensitive balance, we may find that its mass is 6.723 g. This means its mass lies between 6.722 and 6.724 grams, an uncertainty of 0.001 gram. Every measurement has some uncertainty    , which depends on the device used (and the user’s ability). All of the digits in a measurement, including the uncertain last digit, are called significant figures    or significant digits . Note that zero may be a measured value; for example, if you stand on a scale that shows weight to the nearest pound and it shows “120,” then the 1 (hundreds), 2 (tens) and 0 (ones) are all significant (measured) values.

Questions & Answers

how does the symbolic work
Princess Reply
how do you work out the practicals
Ann Reply
how many grams of calcium contain atoms of calcium equal to iron atoms in 5.6g of iron
Soni Reply
what is d meaning of organic chemistry
Elizabeth Reply
it's a compound that comprises of hydrocarbon
what iz alkanol
icha Reply
alkanol there are organic compounds with the functional group of ROH and relative molecular formula (CnH2n+1+OH)
ok tnk u
you are welcome
Sam. A
What's alkaline soil
Amoo Reply
a system in which only energy is transferred between the system and the surrounding is called?
Ani Reply
which Element exhibit diagonal relationship with aluminum
following processes: Solid phosphorus pentachloride decomposes to liquid phosphorus trichloride and chlorine gas b. Deep blue solid copper(II) sulfate pentahydrate is heated to drive off water vapor to form white solid copper(II) sulfate
Hisham Reply
How to know periodic table oftend
Ahmed Reply
u can know it through singing it as song it simple
or making acronyms from it
how to get atomic number of an element
Ogunleye Reply
how do you solve the examples in a much more explanatory way
it seems by multiplying d number of d element by 2
E.g like carbon 6*2=12 so d atomic number is 12
The reaction of aceto nitrile with propane in the presence of the acid
Explain this paragraph in short
Manish Reply
What is solid state?
Manish Reply
What is chemical reaction
transforming reactants to product(s)
solid state is composed of tightly particles and it has a definite shape and volume
Example of Lewis acid
Chidera Reply
Example of Lewis acid
Anything with an empty orbital... the hydrogen ion is the most common example. BH3 is the typical example, but any metal in a coordination complex can be considered a Lewis acid.
okay thanks
aluminium and sulphur react to give aluminium sulfide.How many grams of Al are required to produce 100g of aluminium sulphide
Soni Reply
aluminium and sulphur react to give aluminium sulphide how many grams of Al are required to produce 100g of aluminium sulphide?
aluminium and sulphur react to give aluminium sulphide how many grams of Al are required to produce 100g of aluminium sulphide?
150 comes from?
thank you very much
molar mass of Al2S3
what's periodic table
Practice Key Terms 6

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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