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For example,

Equal Measurements Unit Fraction
1ft = 12in. size 12{"1ft"="12in"} {} 1ft 12in. or 12in. 1ft size 12{ { {"1ft"} over {"12in."} } "or" { {"12in."} over {"1ft"} } } {}
1pt = 16 fl oz size 12{"1pt"="16 fl oz"} {} 1pt 16 fl oz or 16 fl oz 1pt size 12{ { {"1pt"} over {"16 fl oz"} } " or " { {"16 fl oz"} over {"1pt"} } } {}
1wk = 7da size 12{"1wk"="7da"} {} 7da 1wk or 1wk 7da size 12{ { {"7da"} over {"1wk"} } " or " { {"1wk"} over {"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 yd = 3 ft size 12{1" yd "="3 ft"} {} . There are two corresponding unit fractions, 1 yd 3 ft size 12{ { {"1 yd"} over {"3 ft"} } } {} and 3 ft 1 yd size 12{ { {"3 ft"} over {"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 3 ft 1 yd size 12{ { {"3 ft"} over {"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.

11 yd = 11 yd 1 3 ft 1yd Divide out common units. = 11 yd 1 3 ft 1 yd (Units can be added, subtracted, multiplied, and divided, just as numbers can.) = 11 3 ft 1 = 33 ft

Thus, 11 yd = 33 ft .

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Convert 36 fl oz to pints.

Looking in the unit conversion table under liquid volume , we see that 1 pt = 16 fl oz size 12{"1 pt "=" 16 fl oz"} {} . Since we are to convert to pints, we will construct a unit fraction with pints in the numerator.

36 fl oz = 36 fl oz 1 1 pt 16 fl oz Divide out common units. = 36 fl oz 1 1 pt 16 fl oz = 36 1 pt 16 = 36 pt 16 Reduce. = 9 4 pt Convert to decimals: 9 4 = 2.25 .

Thus, 36 fl oz = 2 . 25 pt size 12{"36 fl oz "=" 2" "." "25 pt"} {} .

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Convert 2,016 hr to weeks.

Looking in the unit conversion table under time , we see that 1wk = 7da size 12{"1wk "="7da"} {} and that 1 da = 24 hr size 12{1" da "=" 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 1 da 24 hr size 12{ { {"1 da"} over {"24 hr"} } } {} . The unit fraction needed for converting from days to weeks is 1 wk 7 da size 12{ { {"1 wk"} over {"7 da"} } } {} .

2,016 hr = 2,016 hr 1 1 da 24 hr 1 wk 7 da Divide out common units. = 2,016 hr 1 1 da 24 hr 1 wk 7 da = 2,016 1 wk 24 7 Reduce. = 12 wk

Thus, 2,016 hr = 12 wk size 12{"2,016 hr "=" 12 wk"} {} .

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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

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Convert 2 mi to feet.

10,560 ft

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Convert 26 ft to yards.

8.67 yd

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Convert 9 qt to pints.

18 pt

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Convert 52 min to hours.

0.87 hr

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Convert 412 hr to weeks.

2.45 wk

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Exercises

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

8 mi to inches

506,880 inches

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5 in. to yards

0.14 yard

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62 in. to miles

0.00 miles (to two decimal places)

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6 T to ounces

192,000 ounces

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15,000 oz to pounds

937.5 pounds

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9 tbsp to teaspoons

27 teaspoons

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5 pt to fluid ounces

80 fluid ounces

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5 fl oz to quarts

0.16 quart

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5 pt to teaspoons

480 teaspoons

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18 min to seconds

1,080 seconds

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3 hr to days

1 8 = 0 . 125 size 12{ { {1} over {8} } =0 "." "125"} {} day

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1 2 da to weeks

1 14 = 0 . 0714 size 12{ { {1} over {"14"} } =0 "." "0714"} {} week

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Exercises for review

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

1,2,4,5,8

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( [link] ) Find 2 4 5 size 12{2 { {4} over {5} } } {} of 5 5 6 size 12{5 { {5} over {6} } } {} of 7 5 7 size 12{7 { {5} over {7} } } {} .

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( [link] ) Convert 0 . 3 2 3 size 12{0 "." 3 { {2} over {3} } } {} to a fraction.

11 30 size 12{ { {"11"} over {"30"} } } {}

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( [link] ) Use the clustering method to estimate the sum: 53 + 82 + 79 + 49 size 12{"53"+"82"+"79"+"49"} {} .

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( [link] ) Use the distributive property to compute the product: 60 46 size 12{"60" cdot "46"} {} .

60 ( 50 4 ) = 3, 000 240 = 2, 760 size 12{"60" \( "50" - 4 \) =3,"000" - "240"=2,"760"} {}

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Questions & Answers

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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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
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
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
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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