# 9.1 Measurement and the united states system  (Page 2/2)

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For example,

 Equal Measurements Unit Fraction $\text{1ft}=\text{12in.}$ $\frac{\text{1ft}}{\text{12in.}}\text{or}\frac{\text{12in.}}{\text{1ft}}$ $\text{1pt}=\text{16 fl oz}$ $\frac{\text{1pt}}{\text{16 fl oz}}\text{or}\frac{\text{16 fl oz}}{\text{1pt}}$ $\text{1wk}=\text{7da}$ $\frac{\text{7da}}{\text{1wk}}\text{or}\frac{\text{1wk}}{\text{7da}}$

## Sample set a

Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

Convert 11 yards to feet.

Looking in the unit conversion table under length , we see that $1\text{yd}=\text{3 ft}$ . There are two corresponding unit fractions, $\frac{\text{1 yd}}{\text{3 ft}}$ and $\frac{\text{3 ft}}{\text{1 yd}}$ . Which one should we use? Look to see which unit we wish to convert to. Choose the unit fraction with this unit in the numerator . We will choose $\frac{\text{3 ft}}{\text{1 yd}}$ since this unit fraction has feet in the numerator. Now, multiply 11 yd by the unit fraction. Notice that since the unit fraction has the value of 1, multiplying by it does not change the value of 11 yd.

$\begin{array}{cccc}\hfill 11\text{yd}& =& \frac{\text{11}\text{yd}}{1}\cdot \frac{3\text{ft}}{\text{1yd}}\hfill & \text{Divide out common units.}\hfill \\ & =& \frac{11\overline{)\text{yd}}}{1}\cdot \frac{3\text{ft}}{1\overline{)\text{yd}}}\hfill & \text{(Units can be added, subtracted, multiplied, and divided, just as numbers can.)}\hfill \\ & =& \frac{11\cdot 3\text{ft}}{1}\hfill & \\ & =& 33\text{ft}\hfill & \end{array}$

Thus, $11\text{yd}=33\text{ft}$ .

Convert 36 fl oz to pints.

Looking in the unit conversion table under liquid volume , we see that $\text{1 pt}=\text{16 fl oz}$ . Since we are to convert to pints, we will construct a unit fraction with pints in the numerator.

$\begin{array}{cccc}\hfill 36\text{fl oz}& =\hfill & \frac{36\text{fl oz}}{1}\cdot \frac{1\text{pt}}{16\text{fl oz}}& \text{Divide out common units.}\hfill \\ & =& \frac{36\overline{)\text{fl oz}}}{1}\cdot \frac{1\text{pt}}{16\overline{)\text{fl oz}}}\hfill & \\ & =& \frac{36\cdot \text{1 pt}}{16}\hfill & \\ & =& \frac{\text{36 pt}}{16}\hfill & \text{Reduce.}\hfill \\ & =& \frac{9}{4}\text{pt}\hfill & \text{Convert to decimals:}\frac{9}{4}=2.25.\hfill \end{array}$

Thus, $\text{36 fl oz}=\text{2}\text{.}\text{25 pt}$ .

Convert 2,016 hr to weeks.

Looking in the unit conversion table under time , we see that $\text{1wk}=\text{7da}$ and that $1\text{da}=\text{24 hr}$ . To convert from hours to weeks, we must first convert from hours to days and then from days to weeks. We need two unit fractions.

The unit fraction needed for converting from hours to days is $\frac{\text{1 da}}{\text{24 hr}}$ . The unit fraction needed for converting from days to weeks is $\frac{\text{1 wk}}{\text{7 da}}$ .

$\begin{array}{cccc}\hfill 2,016\text{hr}& =& \frac{2,016\text{hr}}{1}\cdot \frac{1\text{da}}{24\text{hr}}\cdot \frac{1\text{wk}}{7\text{da}}\hfill & \text{Divide out common units.}\hfill \\ & =& \frac{2,016\overline{)\text{hr}}}{1}\cdot \frac{1\overline{)\text{da}}}{24\overline{)\text{hr}}}\cdot \frac{1\text{wk}}{7\overline{)\text{da}}}\hfill & \hfill \\ & =& \frac{2,016\cdot 1\text{wk}}{24\cdot 7}\hfill & \text{Reduce.}\hfill \\ & =& 12\text{wk}\hfill & \end{array}$

Thus, $\text{2,016 hr}=\text{12 wk}$ .

## Practice set a

Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

Convert 18 ft to yards.

6 yd

Convert 2 mi to feet.

10,560 ft

Convert 26 ft to yards.

8.67 yd

Convert 9 qt to pints.

18 pt

Convert 52 min to hours.

0.87 hr

Convert 412 hr to weeks.

2.45 wk

## Exercises

Make each conversion using unit fractions. If fractions occur, convert them to decimals rounded to two decimal places.

14 yd to feet

42 feet

3 mi to yards

8 mi to inches

506,880 inches

2 mi to inches

18 in. to feet

1.5 feet

84 in. to yards

5 in. to yards

0.14 yard

106 ft to miles

62 in. to miles

0.00 miles (to two decimal places)

0.4 in. to yards

3 qt to pints

6 pints

5 lb to ounces

6 T to ounces

192,000 ounces

4 oz to pounds

15,000 oz to pounds

937.5 pounds

15,000 oz to tons

9 tbsp to teaspoons

27 teaspoons

3 c to tablespoons

5 pt to fluid ounces

80 fluid ounces

16 tsp to cups

5 fl oz to quarts

0.16 quart

3 qt to gallons

5 pt to teaspoons

480 teaspoons

3 qt to tablespoons

18 min to seconds

1,080 seconds

4 days to hours

3 hr to days

$\frac{1}{8}=0\text{.}\text{125}$ day

$\frac{1}{2}$ hr to days

$\frac{1}{2}$ da to weeks

$\frac{1}{\text{14}}=0\text{.}\text{0714}$ week

$3\frac{1}{7}$ wk to seconds

## Exercises for review

( [link] ) Specify the digits by which 23,840 is divisible.

1,2,4,5,8

( [link] ) Find $2\frac{4}{5}$ of $5\frac{5}{6}$ of $7\frac{5}{7}$ .

( [link] ) Convert $0\text{.}3\frac{2}{3}$ to a fraction.

$\frac{\text{11}}{\text{30}}$

( [link] ) Use the clustering method to estimate the sum: $\text{53}+\text{82}+\text{79}+\text{49}$ .

( [link] ) Use the distributive property to compute the product: $\text{60}\cdot \text{46}$ .

$\text{60}\left(\text{50}-4\right)=3,\text{000}-\text{240}=2,\text{760}$

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
7hours 36 min - 4hours 50 min
Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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