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Practice set c

Perform each multiplication.

( 3 × 10 5 ) ( 2 × 10 12 )

6 × 10 17

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( 1 × 10 4 ) ( 6 × 10 24 )

6 × 10 20

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( 5 × 10 18 ) ( 3 × 10 6 )

1.5 × 10 25

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( 2.1 × 10 9 ) ( 3 × 10 11 )

6.3 × 10 20

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Exercises

Convert the numbers used in the following problems to scientific notation.

Mount Kilimanjaro is the highest mountain in Africa. It is 5890 meters high.

5.89 × 10 3

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The planet Mars is about 222,900,000,000 meters from the sun.

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There is an irregularly shaped galaxy, named NGC 4449, that is about 250,000,000,000,000,000,000,000 meters from earth.

2.5 × 10 23

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The farthest object astronomers have been able to see (as of 1981) is a quasar named 3C427. There seems to be a haze beyond this quasar that appears to mark the visual boundary of the universe. Quasar 3C427 is at a distance of 110,000,000,000,000,000,000,000,000 meters from the earth.

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The smallest known insects are about the size of a typical grain of sand. They are about 0.0002 meters in length (2 ten-thousandths of a meter).

2 × 10 4

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Atoms such as hydrogen, carbon, nitrogen, and oxygen are about 0.0000000001 meter across.

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The island of Manhattan, in New York, is about 57,000 square meters in area.

5.7 × 10 4

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The second largest moon of Saturn is Rhea. Rhea has a surface area of about 735,000 square meters, roughly the same surface area as Australia.

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A star, named Epsilon Aurigae B, has a diameter (distance across) of 2,800,000,000,000 meters. This diameter produces a surface area of about 24,630,000,000,000,000,000,000,000 square meters. This star is what astronomers call a red giant and it is the largest red giant known. If Epsilon Aurigae were placed at the sun’s position, its surface would extend out to the planet Uranus.

2.8 × 10 12 , 2.463 × 10 25

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The volume of the planet Venus is 927,590,000,000,000,000,000 cubic meters.

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The average mass of a newborn American female is about 3360 grams.

3.36 × 10 3

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The largest brain ever measured was that of a sperm whale. It had a mass of 9200 grams.

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The mass of the Eiffel tower in Paris, France, is 8,000,000 grams.

8 × 10 6

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In 1981, a Japanese company built the largest oil tanker to date. The ship has a mass of about 510,000,000,000 grams. This oil tanker is more than 6 times as massive as the U.S. aircraft carrier, U.S.S. Nimitz .

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In the constellation of Virgo, there is a cluster of about 2500 galaxies. The combined mass of these galaxies is 150,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 grams.

1.5 × 10 62

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The mass of an amoeba is about 0.000004 gram.

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Cells in the human liver have masses of about 0.000000008 gram.

8 × 10 9

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The human sperm cell has a mass of about 0.000000000017 gram.

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The principal protein of muscle is myosin. Myosin has a mass of 0.00000000000000000103 gram.

1.03 × 10 18

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Amino acids are molecules that combine to make up protein molecules. The amino acid tryptophan has a mass of 0.000000000000000000000340 gram.

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An atom of the chemical element bromine has 35 electrons. The mass of a bromine atom is 0.000000000000000000000000031 gram.

3.1 × 10 26

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Physicists are performing experiments that they hope will determine the mass of a small particle called a neutrino. It is suspected that neutrinos have masses of about 0.0000000000000000000000000000001 gram.

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The approximate time it takes for a human being to die of asphyxiation is 316 seconds.

3.16 × 10 2

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On the average, the male housefly lives 1,468,800 seconds (17 days).

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Aluminum-26 has a half-life of 740,000 years.

7.4 × 10 5

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Manganese-53 has a half-life of 59,918,000,000,000 seconds (1,900,000 years).

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In its orbit around the sun, the earth moves a distance one and one half feet in about 0.0000316 second.

3.16 × 10 5

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A pi-meson is a subatomic particle that has a half-life of about 0.0000000261 second.

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A subatomic particle called a neutral pion has a half-life of about 0.0000000000000001 second.

1 × 10 16

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Near the surface of the earth, the speed of sound is 1195 feet per second.

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For the following problems, convert the numbers from scientific notation to standard decimal form.

The sun is about 1 × 10 8 meters from earth.

100 , 000 , 000

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The mass of the earth is about 5.98 × 10 27 grams.

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Light travels about 5.866 × 10 12 miles in one year.

5 , 866 , 000 , 000 , 000

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One year is about 3 × 10 7 seconds.

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Rubik’s cube has about 4.3 × 10 19 different configurations.

43 , 000 , 000 , 000 , 000 , 000 , 000

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A photon is a particle of light. A 100-watt light bulb emits 1 × 10 20 photons every second.

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There are about 6 × 10 7 cells in the retina of the human eye.

60 , 000 , 000

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A car traveling at an average speed will travel a distance about equal to the length of the smallest fingernail in 3.16 × 10 4 seconds.

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A ribosome of E. coli has a mass of about 4.7 × 10 19 grams.

0.00000000000000000047

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A mitochondrion is the energy-producing element of a cell. A mitochondrion is about 1.5 × 10 6 meters in diameter.

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There is a species of frogs in Cuba that attain a length of at most 1.25 × 10 2 meters.

0.0125

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Perform the following operations.

( 2 × 10 4 ) ( 3 × 10 5 )

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( 4 × 10 2 ) ( 8 × 10 6 )

3.2 × 10 9

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( 6 × 10 14 ) ( 6 × 10 10 )

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( 3 × 10 5 ) ( 8 × 10 7 )

2.4 × 10 3

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( 2 × 10 1 ) ( 3 × 10 5 )

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( 9 × 10 5 ) ( 1 × 10 11 )

9 × 10 16

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( 3.1 × 10 4 ) ( 3.1 × 10 6 )

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( 4.2 × 10 12 ) ( 3.6 × 10 20 )

1.512 × 10 31

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( 5.9 × 10 14 ) 2

3.481 × 10 29

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( 8.8 × 10 50 ) 2

7.744 × 10 99

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If Mount Kilimanjaro was 1,000,000 times as high as it really is, how high would it be? (See problem 1.)

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If the planet Mars was 300,000 times as far from the sun as it really is, how far from the sun would it be? (See problem 2.)

6.687 × 10 16

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If 800,000,000 of the smallest insects known were lined up head to tail, how far would they stretch? (See problem 5.)

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If Rhea, the moon of Saturn, had a surface area 0.00000000002 of its real surface area, what would that surface area be? (See problem 8.)

1.47 × 10 5

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If the star Epsilon Aurigae B had a surface area 0.005 of its real surface area, what would that surface area be? (See problem 9.)

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If the mass of all the galaxies in the constellation Virgo was only 0.0000000000000000000000003 of its real mass, what would that mass be? (See problem 15.)

4.5 × 10 37

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What is the mass of 15,000,000,000,000 bromine atoms? (See problem 21.)

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Exercises for review

( [link] ) What integers can replace x so that the statement 6 < x < 2 is true?

5 , 4 , 3

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( [link] ) Simplify ( 5 x 2 y 4 ) ( 2 x y 5 )

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( [link] ) Determine the value of [ ( | 5 | ) ] .

5

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( [link] ) Write x 3 y 5 z 4 so that only positive exponents appear.

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( [link] ) Write ( 2 z + 1 ) 3 ( 2 z + 1 ) 5 so that only positive exponents appear.

1 ( 2 z + 1 ) 2

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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