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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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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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