3.7 Scientific notation  (Page 3/3)

$(3\times {10}^5)(2\times {10}^{12})$

$(1\times {10}^{-4})(6\times {10}^{24})$

$(5\times {10}^{18})(3\times {10}^6)$

$(2.1\times {10}^{-9})(3\times {10}^{-11})$

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

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

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

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.

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).

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

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

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.

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.

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

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

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

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

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 .

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.

The mass of an amoeba is about $0.000004$ gram.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

The sun is about $1\times {10}^8$ meters from earth.

The mass of the earth is about $5.98\times {10}^{27}$ grams.

Light travels about $5.866\times {10}^{12}$ miles in one year.

One year is about $3\times {10}^7$ seconds.

Rubik’s cube has about $4.3\times {10}^{19}$ different configurations.

A photon is a particle of light. A 100-watt light bulb emits $1\times {10}^{20}$ photons every second.

There are about $6\times {10}^7$ cells in the retina of the human eye.

A car traveling at an average speed will travel a distance about equal to the length of the smallest fingernail in $3.16\times {10}^{-4}$ seconds.

A ribosome of E. coli has a mass of about $4.7\times {10}^{-19}$ grams.

A mitochondrion is the energy-producing element of a cell. A mitochondrion is about $1.5\times {10}^{-6}$ meters in diameter.

There is a species of frogs in Cuba that attain a length of at most $1.25\times {10}^{-2}$ meters.

$(2\times {10}^4)(3\times {10}^5)$

$(4\times {10}^2)(8\times {10}^6)$

$(6\times {10}^{14})(6\times {10}^{-10})$

$(3\times {10}^{-5})(8\times {10}^7)$

$(2\times {10}^{-1})(3\times {10}^{-5})$

$(9\times {10}^{-5})(1\times {10}^{-11})$

$(3.1\times {10}^4)(3.1\times {10}^{-6})$

$(4.2\times {10}^{-12})(3.6\times {10}^{-20})$

${(1.1\times {10}^6)}^2$

${(5.9\times {10}^{14})}^2$

${(1.02\times {10}^{-17})}^2$

${(8.8\times {10}^{-50})}^2$

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

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.)

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

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.)

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.)

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.)

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

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

( [link] ) Simplify $(5x^2{y}^4)(2x{y}^5)$

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

( [link] ) Write $\frac{x^3{y}^{-5}}{z^{-4}}$ so that only positive exponents appear.

( [link] ) Write ${(2z+1)}^3{(2z+1)}^{-5}$ so that only positive exponents appear.