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Figures A through C each show targets with holes where the arrows hit. The archer in figure A was both accurate and precise as all 3 arrows are clustered in the center of the target. In figure B, the archer is precise but not accurate, as all 3 arrows are clustered together but to the upper right of the center of the target. In Figure C, the archer is neither accurate nor precise as the 3 holes are not close together and are located both to the upper right and right of the target.
(a) These arrows are close to both the bull’s eye and one another, so they are both accurate and precise. (b) These arrows are close to one another but not on target, so they are precise but not accurate. (c) These arrows are neither on target nor close to one another, so they are neither accurate nor precise.

Suppose a quality control chemist at a pharmaceutical company is tasked with checking the accuracy and precision of three different machines that are meant to dispense 10 ounces (296 mL) of cough syrup into storage bottles. She proceeds to use each machine to fill five bottles and then carefully determines the actual volume dispensed, obtaining the results tabulated in [link] .

Volume (mL) of Cough Medicine Delivered by 10-oz (296 mL) Dispensers
Dispenser #1 Dispenser #2 Dispenser #3
283.3 298.3 296.1
284.1 294.2 295.9
283.9 296.0 296.1
284.0 297.8 296.0
284.1 293.9 296.1

Considering these results, she will report that dispenser #1 is precise (values all close to one another, within a few tenths of a milliliter) but not accurate (none of the values are close to the target value of 296 mL, each being more than 10 mL too low). Results for dispenser #2 represent improved accuracy (each volume is less than 3 mL away from 296 mL) but worse precision (volumes vary by more than 4 mL). Finally, she can report that dispenser #3 is working well, dispensing cough syrup both accurately (all volumes within 0.1 mL of the target volume) and precisely (volumes differing from each other by no more than 0.2 mL).

Key concepts and summary

Quantities can be exact or measured. Measured quantities have an associated uncertainty that is represented by the number of significant figures in the measurement. The uncertainty of a calculated value depends on the uncertainties in the values used in the calculation and is reflected in how the value is rounded. Measured values can be accurate (close to the true value) and/or precise (showing little variation when measured repeatedly).

Chemistry end of chapter exercises

Express each of the following numbers in scientific notation with correct significant figures:

(a) 711.0

(b) 0.239

(c) 90743

(d) 134.2

(e) 0.05499

(f) 10000.0

(g) 0.000000738592

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Express each of the following numbers in exponential notation with correct significant figures:

(a) 704

(b) 0.03344

(c) 547.9

(d) 22086

(e) 1000.00

(f) 0.0000000651

(g) 0.007157

(a) 7.04 × 10 2 ; (b) 3.344 × 10 −2 ; (c) 5.479 × 10 2 ; (d) 2.2086 × 10 4 ; (e) 1.00000 × 10 3 ; (f) 6.51 × 10 −8 ; (g) 7.157 × 10 −3

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Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

(a) the number of eggs in a basket

(b) the mass of a dozen eggs

(c) the number of gallons of gasoline necessary to fill an automobile gas tank

(d) the number of cm in 2 m

(e) the mass of a textbook

(f) the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h

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Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:

(a) the number of seconds in an hour

(b) the number of pages in this book

(c) the number of grams in your weight

(d) the number of grams in 3 kilograms

(e) the volume of water you drink in one day

(f) the distance from San Francisco to Kansas City

(a) exact; (b) exact; (c) uncertain; (d) exact; (e) uncertain; (f) uncertain

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How many significant figures are contained in each of the following measurements?

(a) 38.7 g

(b) 2 × 10 18 m

(c) 3,486,002 kg

(d) 9.74150 × 10 −4 J

(e) 0.0613 cm 3

(f) 17.0 kg

(g) 0.01400 g/mL

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How many significant figures are contained in each of the following measurements?

(a) 53 cm

(b) 2.05 × 10 8 m

(c) 86,002 J

(d) 9.740 × 10 4 m/s

(e) 10.0613 m 3

(f) 0.17 g/mL

(g) 0.88400 s

(a) two; (b) three; (c) five; (d) four; (e) six; (f) two; (g) five

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The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.

(a) 0.0055 g active ingredients

(b) 12 tablets

(c) 3% hydrogen peroxide

(d) 5.5 ounces

(e) 473 mL

(f) 1.75% bismuth

(g) 0.001% phosphoric acid

(h) 99.80% inert ingredients

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Round off each of the following numbers to two significant figures:

(a) 0.436

(b) 9.000

(c) 27.2

(d) 135

(e) 1.497 × 10 −3

(f) 0.445

(a) 0.44; (b) 9.0; (c) 27; (d) 140; (e) 1.5 × 10 −3 ; (f) 0.44

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Round off each of the following numbers to two significant figures:

(a) 517

(b) 86.3

(c) 6.382 × 10 3

(d) 5.0008

(e) 22.497

(f) 0.885

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Perform the following calculations and report each answer with the correct number of significant figures.

(a) 628 × 342

(b) (5.63 × 10 2 ) × (7.4 × 10 3 )

(c) 28.0 13.483

(d) 8119 × 0.000023

(e) 14.98 + 27,340 + 84.7593

(f) 42.7 + 0.259

(a) 2.15 × 10 5 ; (b) 4.2 × 10 6 ; (c) 2.08; (d) 0.19; (e) 27,440; (f) 43.0

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Perform the following calculations and report each answer with the correct number of significant figures.

(a) 62.8 × 34

(b) 0.147 + 0.0066 + 0.012

(c) 38 × 95 × 1.792

(d) 15 – 0.15 – 0.6155

(e) 8.78 × ( 0.0500 0.478 )

(f) 140 + 7.68 + 0.014

(g) 28.7 – 0.0483

(h) ( 88.5 87.57 ) 45.13

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Consider the results of the archery contest shown in this figure.

(a) Which archer is most precise?

(b) Which archer is most accurate?

(c) Who is both least precise and least accurate?

4 targets are shown each with 4 holes indicating where the arrows hit the targets. Archer W put all 4 arrows closely around the center of the target. Archer X put all 4 arrows in a tight cluster but far to the lower right of the target. Archer Y put all 4 arrows at different corners of the target. All 4 arrows are very far from the center of the target. Archer Z put 2 arrows close to the target and 2 other arrows far outside of the target.

(a) Archer X; (b) Archer W; (c) Archer Y

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Classify the following sets of measurements as accurate, precise, both, or neither.

(a) Checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g

(b) Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL

(c) Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%

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Questions & Answers

An atom or group of atoms bearing anelectrical charge such as the sodium and chlorine atoms in a salt solution.
Adazion Reply
Hello guys! Answer me questions nah
Adazion
pls wat is periodic table
Prince
it's a list that shows the chemical element arranged according to their properties.
Adazion Reply
what is the chemical equation for ideal gas?
Adazion
what's Boyle and gas law?
Adazion
what's the meaning of this℃ in atomic table
Adazion
wat are ions
Sinyene
What is periodic table
SIRAJO Reply
Table that shows the elements in order of their atomic number
Uzair
organization of everything known in the universe in groups and periods. The structure is based on increasing mass and reaction properties.
Kate
How to mix chemical
Ukeh Reply
why the elements of group 7 are called Noble gases
isaac Reply
they aren't. group 8 is the noble gasses. they are snobs that don't mix with others like nobles, they have full valence shells so they don't form bonds with other elements easily. nobles don't mingle with the common folk...
Jessica
the group 7elements are not the noble gases . according to modern periodic group 18 are called noble gases elements because their valence shell are completely field so that they can't gain or loss electron so they are not able to involve in any chemical reaction.
Leena
Group 7 element they are not noble gases they halogen and halogen mean salt formers
SIRAJO
what is chemistry
Daniel Reply
chemistry is the branch of science which deal with the composition of matter
SHEDRACK
chemistry is an organized way to think about matter
Kate
Chemistry is the branch of science that deals with the composition, properties and uses of matter
Bamgbose
The branch of science concerned with the substances of which matter is composed, the investigation of their properties and reactions, and the use of such reactions to form new substances.
Aminu
discuss the orbital stracture of the following methane,ethane,ethylene,acetylene
khadija Reply
Why phosphurs in solid state have one atom but in gas state have four atoms
Shehab Reply
Are nuclear reactions both exothermic reactions and endothermic reactions or what?
Blessed Reply
to what volume must 8.32 NaOH be diluted to its analytical concentration 0.20 M
Sheriza Reply
weight in mg 1.76 mole of I
Sheriza
the types of hydrocarbons
Ohanaka Reply
u are mad go and open textbook
Emmanuel
hahahahahahahahahahahahaha
Jessica
aliphatic and aromatic hydrocarbons
Osakue
stupid boy Emmanuel
Ohanaka
saturated and unsaturated
Leena
aromatic hydrocarbon aliphatic hydrocarbon
SIRAJO
I don't use to see the messages
Adazion Reply
Hhhhhh
SIRAJO
how can you determine the electronegativity of a compound or in molecules
Shalom Reply
when u move from left to right in a periodic table the negativity increases
reeza
Are you trying to say that the elctronegativity increases down the group and decreases across the period?
Ohanaka
yes and also increases across the period
reeza
for instance when you look at one group of elements in a periodic table electronegativity decreases when you go across the table electronegativity increases. hydrogen is more electronegative than sodium, potassium of that group. oxygen is more electronegative than carbon.
reeza
i hope we all know that organic compounds have carbon as their back bone
Madueke
OK,Thank you so much for the answer. I am happy now
Adazion Reply
can I ask you a question now
Osakue
yes
hanna
what is the oxidation number of nitrogen, oxygen and sulphur
Osakue
5, -2 & -2
hanna
What is periodic table
SIRAJO
What is an atom?
Adazion Reply
is a smallest particle of a chemical element that can exist
Osakue
can I ask a question
Osakue
it is a substance that cannot be broken down into simpler units by any chemical reaction
Madueke
An atom is the smallest part of an element dat can take part in chemical reaction.
Idris
an atom is the smallest part of an element that can take part in a chemical reaction nd still retain it chemical properties
Precious
Is the smallest particles of an element that take part in chemical reaction without been change
John
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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