# 1.1 Accuracy, precision, and significant figures  (Page 6/12)

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## Conceptual questions

What is the relationship between the accuracy and uncertainty of a measurement?

Prescriptions for vision correction are given in units called diopters (D). Determine the meaning of that unit. Obtain information (perhaps by calling an optometrist or performing an internet search) on the minimum uncertainty with which corrections in diopters are determined and the accuracy with which corrective lenses can be produced. Discuss the sources of uncertainties in both the prescription and accuracy in the manufacture of lenses.

## Problems&Exercises

Express your answers to problems in this section to the correct number of significant figures and proper units.

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

2 kg

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

(a) A car speedometer has a $5.0\text{%}$ uncertainty. What is the range of possible speeds when it reads $\text{90}\phantom{\rule{0.25em}{0ex}}\text{km/h}$ ? (b) Convert this range to miles per hour. $\left(\text{1 km}=\text{0.6214 mi}\right)$

1. $\text{85}\text{.}5\phantom{\rule{0.25em}{0ex}}\text{to 94}\text{.}\text{5 km/h}$
2. $\text{53}\text{.}1\phantom{\rule{0.25em}{0ex}}\text{to 58}\text{.}\text{7 mi/h}$

An infant’s pulse rate is measured to be $\text{130}±5$ beats/min. What is the percent uncertainty in this measurement?

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

(a)

(b)

(c)

A can contains 375 mL of soda. How much is left after 308 mL is removed?

State how many significant figures are proper in the results of the following calculations: (a) $\left(\text{106}\text{.}7\right)\left(\text{98}\text{.}2\right)/\left(\text{46}\text{.}\text{210}\right)\left(1\text{.}\text{01}\right)$ (b) ${\left(\text{18}\text{.}7\right)}^{2}$ (c) $\left(1\text{.}\text{60}×{\text{10}}^{-\text{19}}\right)\left(\text{3712}\right)$ .

1. 3
2. 3
3. 3

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

(a) If your speedometer has an uncertainty of $2\text{.}0\phantom{\rule{0.25em}{0ex}}\text{km/h}$ at a speed of $\text{90}\phantom{\rule{0.25em}{0ex}}\text{km/h}$ , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads $\text{60}\phantom{\rule{0.25em}{0ex}}\text{km/h}$ , what is the range of speeds you could be going?

a) $2\text{.}2\text{%}$

(b) $\text{59 to 61 km/h}$

(a) A person’s blood pressure is measured to be $\text{120}±2\phantom{\rule{0.25em}{0ex}}\text{mm Hg}$ . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of $\text{80}\phantom{\rule{0.25em}{0ex}}\text{mm Hg}$ ?

A person measures his or her heart rate by counting the number of beats in $\text{30}\phantom{\rule{0.25em}{0ex}}\text{s}$ . If $\text{40}±1$ beats are counted in $\text{30}\text{.}0±0\text{.}5\phantom{\rule{0.25em}{0ex}}\text{s}$ , what is the heart rate and its uncertainty in beats per minute?

$\text{80}±3\phantom{\rule{0.25em}{0ex}}\text{beats/min}$

What is the area of a circle $3\text{.}\text{102}\phantom{\rule{0.25em}{0ex}}\text{cm}$ in diameter?

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

$2\text{.}8\phantom{\rule{0.25em}{0ex}}\text{h}$

A marathon runner completes a $\text{42}\text{.}\text{188}\text{-km}$ course in $2\phantom{\rule{0.25em}{0ex}}\text{h}$ , 30 min, and $\text{12}\phantom{\rule{0.25em}{0ex}}\text{s}$ . There is an uncertainty of $\text{25}\phantom{\rule{0.25em}{0ex}}\text{m}$ in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

The sides of a small rectangular box are measured to be $1\text{.}\text{80}±0\text{.}\text{01}\phantom{\rule{0.25em}{0ex}}\text{cm}$ ,  $2\text{.}\text{05}±0\text{.}\text{02}\phantom{\rule{0.25em}{0ex}}\text{cm, and 3}\text{.}1±0\text{.}\text{1 cm}$ long. Calculate its volume and uncertainty in cubic centimeters.

$\text{11}±1\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{3}$

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where $1\phantom{\rule{0.25em}{0ex}}\text{lbm}=0\text{.}\text{4539}\phantom{\rule{0.25em}{0ex}}\text{kg}$ . (a) If there is an uncertainty of $0\text{.}\text{0001}\phantom{\rule{0.25em}{0ex}}\text{kg}$ in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

The length and width of a rectangular room are measured to be $3\text{.}\text{955}±0\text{.}\text{005}\phantom{\rule{0.25em}{0ex}}\text{m}$ and $3\text{.}\text{050}±0\text{.}\text{005}\phantom{\rule{0.25em}{0ex}}\text{m}$ . Calculate the area of the room and its uncertainty in square meters.

$\text{12}\text{.}\text{06}±0\text{.}\text{04}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$

A car engine moves a piston with a circular cross section of $7\text{.}\text{500}±0\text{.}\text{002}\phantom{\rule{0.25em}{0ex}}\text{cm}$ diameter a distance of $3\text{.}\text{250}±0\text{.}\text{001}\phantom{\rule{0.25em}{0ex}}\text{cm}$ to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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