# 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: $\text{60}\cdot \text{46}$ .

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

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
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what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
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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
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how nano science is used for hydrophobicity
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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..
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what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
In the number 779,844,205 how many ten millions are there?
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
7hours 36 min - 4hours 50 min