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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

what is atomicity
Simbiat Reply
A 45 ml of ph=1,hcl was reacted with a 55l ml of ph=13, naoh solution . what is the final ph
chamini Reply
what is coordination number
YERUMAKULA Reply
coordination number is the number of atoms or ions immediately surrounding a central atom in a complex or crystal
Chidera
what is isotope
Bukar
who is the father of chemistry
Roland Reply
Antoine Lavoisier. Father of modern chemistry
Yapi
Lavoisier
Simbiat
What is geometric isomerism
Imoh Reply
jo
Lakshmi
pls I don't really know teach me
Joel
geometric isomerism are molecules that are locked into their spatial position with respect to one another due to a double Bond or ring structure
Chidera
Chromatography is a physical method of seperation where by mixtures that are in two phrases are separated
Lexzzy Reply
What is chromatography?
Chukwudi Reply
meaning of electrode
DJKRANKY Reply
is ion exchange and ion chromatography the same process?
Vivian
define boyes law and give the formula
Esther Reply
define chemistry and it's properties
Esther
Boyle's law state that at a constant temperature, the pressure of a fixed mass of gas is inversely proportionally to it's volume. P=k/v P1v1=p2v2
MAUREE
Chemistry is the study of matter and it's properties..... It's deals with the composition that governors d use of matter..... Chemistry is also d study of chemical reaction of a substance and it's matter. Properties of chemistry Atom Elements Compound Molecules
MAUREE
chemistry seems more accurately defined as the measurement and study of the interaction / behavior that occurs between any given person place or thing or unit of measure, ie time and energy correlation
Elaine
its the given mass of gas that is inversely proportional to it pressure
Simbiat
Reactive metals are extracted by _______?
Joseph Reply
electrolytic reduction
Amisu
what is ionxide
Wisdom Reply
What is isometrics
Kamaluddeen Reply
Molar mass of aluminum
Victor Reply
why an equation should balanced?
Kwanele Reply
in order to obey the law of conservation of mass
Ibrahim
why does the atomic radius increase across the period
Timothy Reply
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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