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Whenever you make a measurement properly, all the digits in the result are significant. But what if you were analyzing a reported value and trying to determine what is significant and what is not? Well, for starters, all nonzero digits are significant, and it is only zeros that require some thought. We will use the terms “leading,” “trailing,” and “captive” for the zeros and will consider how to deal with them.

The left diagram uses the example of 3090. The zero in the hundreds place is labeled “captive” and the zero in the ones place is labeled trailing. The right diagram uses the example 0.008020. The three zeros in the ones, tenths, and hundredths places are labeled “leading.” The zero in the ten-thousandths place is labeled “captive” and the zero in the millionths place is labeled “trailing.”

Starting with the first nonzero digit on the left, count this digit and all remaining digits to the right. This is the number of significant figures in the measurement unless the last digit is a trailing zero lying to the left of the decimal point.

The left diagram uses the example of 1267 meters. The number 1 is the first nonzero figure on the left. 1267 has 4 significant figures in total. The right diagram uses the example of 55.0 grams. The number 5 in the tens place is the first nonzero figure on the left. 55.0 has 3 significant figures. Note that the 0 is to the right of the decimal point and therefore is a significant figure.

Captive zeros result from measurement and are therefore always significant. Leading zeros, however, are never significant—they merely tell us where the decimal point is located.

The left diagram uses the example of 70.607 milliliters. The number 7 is the first nonzero figure on the left. 70.607 has 5 significant figures in total, as all figures are measured including the 2 zeros. The right diagram uses the example of 0.00832407 M L. The number 8 is the first nonzero figure on the left. 0.00832407 has 6 significant figures.

The leading zeros in this example are not significant. We could use exponential notation (as described in Appendix B) and express the number as 8.32407 × 10 −3 ; then the number 8.32407 contains all of the significant figures, and 10 −3 locates the decimal point.

The number of significant figures is uncertain in a number that ends with a zero to the left of the decimal point location. The zeros in the measurement 1,300 grams could be significant or they could simply indicate where the decimal point is located. The ambiguity can be resolved with the use of exponential notation: 1.3 × 10 3 (two significant figures), 1.30 × 10 3 (three significant figures, if the tens place was measured), or 1.300 × 10 3 (four significant figures, if the ones place was also measured). In cases where only the decimal-formatted number is available, it is prudent to assume that all trailing zeros are not significant.

This figure uses the example of 1300 grams. The one and the 3 are significant figures as they are clearly the result of measurement. The 2 zeros could be significant if they were measured or they could be placeholders.

When determining significant figures, be sure to pay attention to reported values and think about the measurement and significant figures in terms of what is reasonable or likely when evaluating whether the value makes sense. For example, the official January 2014 census reported the resident population of the US as 317,297,725. Do you think the US population was correctly determined to the reported nine significant figures, that is, to the exact number of people? People are constantly being born, dying, or moving into or out of the country, and assumptions are made to account for the large number of people who are not actually counted. Because of these uncertainties, it might be more reasonable to expect that we know the population to within perhaps a million or so, in which case the population should be reported as 3.17 × 10 8 people.

Significant figures in calculations

A second important principle of uncertainty is that results calculated from a measurement are at least as uncertain as the measurement itself. We must take the uncertainty in our measurements into account to avoid misrepresenting the uncertainty in calculated results. One way to do this is to report the result of a calculation with the correct number of significant figures, which is determined by the following three rules for rounding    numbers:

Questions & Answers

give two properties of liquid
Grace Reply
what is measurement
Isaiah Reply
is the comparison of an unknown quantity with a fixed quantity of the same kind
Sahada
How does an element differ from a compound? How are they similar?
Adeola Reply
an element is an indivisible particles that can take part in a reaction and consist of smaller or tiny particles i.e proton, neutrons and electron while a compound is when two or more element chemically combine together. They are similar when they are homogeneous compound. they take the same rxn.
Yusuf
an element is s chemically pure substance containing a particular type of atoms.. A COMPOUND is a substance containing atoms from different elements..
Inemesit
How to get the Lewis formula of SeCl+3
Erica Reply
hi,I'm new here can I join the conversation
EZEA
what is the structural formula for starch
EZEA Reply
Starch is a mixture (of chemicals) of amylose and amylopectin. Both are macromolecules and polymers. You can search on wikipedia.
Abdelkarim
what is the roles of filter bed
Fathmat
what is the roles of Alu m
Fathmat
what is the roles of chlorine
Fathmat
Roles can be classified or correlate it to different areas: For example: Chlorine can be used in reactions (in industry) to manufacture HCl, which then can be used for other things. Or in swimming pools to kill bacteria. Or as a component in compounds with pharmaceutical roles (drugs). For Al:
Abdelkarim
Its dentisty value is suitable to be used in alloys (mixture of metals) in aircraft bodies. Also, Aluminium foils, Tin cans,.. Some of them are also in Al overhead cables in streets and long roads.
Abdelkarim
what is chemistry
Maxamed
what is the meaning of exceedingly
Yushao Reply
it is an adverb which means extremely
Rohini
what is atomic chemistry?
Gladys Reply
Lewis structure for no3
Gladys
Lewis structure for no3
Gladys
what is weak acid
Muhammed Reply
It is an acid which partially ionises in water.
Abdelkarim
what is incandescence
Clifton
what makes it glow
Clifton
why is it red, irange and yellow in color
Clifton
hello am new here and I want to join you
Aliyu
hello
Clifton
hi
Aliyu
too
Gillian
hello i am new here please i want to join this group
Paul
Hi, I'm also new here
Salaudeen
Hi
Keeya
hello guys !!
Sourav
what is pressure?
Slark Reply
The force applied to suction Area of the body
Ahmed
Matter composed of exceedingly small paticle called atom.
Yushao
questions related to metals
Regina Reply
occurrence and preparation of the representatives metals
Regina
list the 20, periodic table and their symbols
Fathmat Reply
hydrogen:h helium;he lithium:l beryllium:be Boron:b Carbon;C Nitrogen:n Oxygen:O FLUORINE:f Neon:n Sodium:s Magnesium:mg Aluminum:a Silicon:s Phosphorus:p Sulphur:s Chlorine:c Argon;a Potassium:p Calcium:c
Benita
Hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, neon, sodium, magnesium, aluminium, silicon, phosphorus, sulphur, chlorine, argon, potassium, calcium
Cudjoe
what is a solute
Ekezie Reply
Any substance that is disolved in a liqid solvent to create a solution
Fifa
sorry liquid
Fifa
it's a liquid substance
Fathmat
hello group
Ayomide
is the substance that dissolves in the solvent
Amos
so is HCl ionic compound
Honest Reply
No, covalent compound ➡️ molecule. As both H and Cl are non-metals and and form covalent bind by sharing valence e-. But can fully ionice in water forming H+ (a proton, a reason for acidity) and Cl- (anion =Chloride) Hydrogen Chloride is a gas at room; Hydrochloric acid = HCl (aq), dissolved in w
Abdelkarim
Form covalenr bond*
Abdelkarim
The question marks are an emoji in the first sentence is an unread emoji. HCl Covalent compund -> molecule
Abdelkarim
Hi.
Queen
Hi
Calvin
Yh
Cudjoe
yes
Amos
what is chemistry
Chukwu Reply
is the study of composition of substances and the way they behave under different conditions
Amos
how do calculate n1 though n6 any help on understanding the concept
Clifton
is the study of properties of matter and it's component
Grace
where can I get the test bank or mcqs ? any idea ?
Sourav 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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