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Squares and other powers

An exponent, or a power, is mathematical shorthand for repeated multiplications. For example, the exponent “2” means to multiply the base for that exponent by itself (in the example here, the base is “5”):

5 2 = 5 × 5 = 25

The exponent is “2” and the base is the number “5.” This expression (multiplying a number by itself) is also called a square. Any number raised to the power of 2 is being squared. Any number raised to the power of 3 is being cubed:

5 3 = 5 × 5 × 5 = 125

A number raised to the fourth power is equal to that number multiplied by itself four times, and so on for higher powers. In general:

n x = n × n x 1

Calculating percents

A percent is a way of expressing a fractional amount of something using a whole divided into 100 parts. A percent is a ratio whose denominator is 100. We use the percent symbol, %, to show percent. Thus, 25% means a ratio of 25 100 , 3% means a ratio of 3 100 , and 100 % percent means 100 100 , or a whole.

Converting percents

A percent can be converted to a fraction by writing the value of the percent as a fraction with a denominator of 100 and simplifying the fraction if possible.

25% = 25 100 = 1 4

A percent can be converted to a decimal by writing the value of the percent as a fraction with a denominator of 100 and dividing the numerator by the denominator.

10% = 10 100 = 0.10

To convert a decimal to a percent, write the decimal as a fraction. If the denominator of the fraction is not 100, convert it to a fraction with a denominator of 100, and then write the fraction as a percent.

0.833 = 833 1000 = 83.3 100 = 83.3%

To convert a fraction to a percent, first convert the fraction to a decimal, and then convert the decimal to a percent.

3 4 = 0.75 = 75 100 = 75%

Suppose a researcher finds that 15 out of 23 students in a class are carriers of Neisseria meningitides . What percentage of students are carriers? To find this value, first express the numbers as a fraction.

carriers total students = 15 23

Then divide the numerator by the denominator.

15 23 = 15 ÷ 23 0.65

Finally, to convert a decimal to a percent, multiply by 100.

0.65 × 100 = 65%

The percent of students who are carriers is 65%.

You might also get data on occurrence and non-occurrence; for example, in a sample of students, 9 tested positive for Toxoplasma antibodies, while 28 tested negative. What is the percentage of seropositive students? The first step is to determine the “whole,” of which the positive students are a part. To do this, sum the positive and negative tests.

positive + negative = 9 + 28 = 37

The whole sample consisted of 37 students. The fraction of positives is:

positive total students = 9 37

To find the percent of students who are carriers, divide the numerator by the denominator and multiply by 100.

9 37 = 9 ÷ 37 0.24 0.24 × 100 = 24%

The percent of positive students is about 24%.

Another way to think about calculating a percent is to set up equivalent fractions, one of which is a fraction with 100 as the denominator, and cross-multiply. The previous example would be expressed as:

9 37 = x 100

Now, cross multiply and solve for the unknown:

Questions & Answers

what is mutation
Cynthia Reply
alteration in genetic makeup
UDEME
Hi, I'm new here. I'm Bello Abdul Hakeem from Nigeria.
BELLO Reply
welcome on board
Kamaluddeen
Thanks brother I'm an undergraduate. I hope to study for MBBS.
BELLO
pls guys help me out
Linda
what is limitation of plate
Linda
limitation of plate load test . there are some that should be considered while performing load test which are given below, this test is usually performed on relatively similar plate ,usually 1 or 2 square foot area the reason is that the plate of greater are the economically not feasible
yemi
Mechanism of bacterial pathogenicity
rashida Reply
Toxicity
Ibrahim
write a short note on Algea
najaatu Reply
green minutes plants organisms that are produced in turf.
Prince
Algae is a kind of a photosynthetic organism, which is usually grown in the moist areas. These are usually the simple plants that grow near to the water bodies. It contains a kind of chlorophyll pigments that act as a primary coloring agent.
Avi
they are eukaryotic and most lived in fresh water. they are photosynthetic that's, they contain chlorophyll and store starch in discrete chloroplast.
Prince
are bacteria important to man
just Reply
yes, depending on the type of bacteria .eg the normal florals, the latic acid batteries etc are important to man
Lois
I mean latic acid bacterial
Lois
I don't understand this topic
Jane Reply
what topic is that
Rose
sahi kon hai bhosri ke
saurabh Reply
define metabolism of carbohydrates with example
Thavasi Reply
what is sterilization a
Sani
the process of keep equipment free from bacteria
shar
is it only bacteria?
Lois
no undesirable fungi and contamination also.
Khushbu
what is streak plate method
Offikwu
what is the biofilm
Dimingu
metabolism is the sum of all the biochemical reaction required for energy generation and use of that energy to synthesize cell materials from small molecules in environment.
Alex
boclenia
Pooja
what are granulocytes
Shawnitta Reply
e.coli
Sukhdeep
granulocytes are type of WBCs which contains granules in the cytoplasm
Owili
what is mutation
Cynthia
it is the interchange of genes from their normal sequence
Esther
is an heritable change of the base-pair sequence of genetic material
Elizabeth
suitable example for prokaryotes
Suvetha Reply
one of the possible early sources of energy was
Suvetha
uv radiation and lighting
Anisha
e coli is the example of prokaryotes
Sukhdeep
archaea too
Noel
which is the specific virus causing typhoid
Jeremiah Reply
it's caused by a virulent bacteria called Salmonella Typhi
Sarah
write the life cycle of HIV
Firomsa Reply
describe the internal and external structure of prokaryotic cell in terms of there appearance and functions
Lenia Reply
compare and contrast similar structures found in prokaryotic and eukaryotic cells
Lenia
control of microorganisms
ISTEFAZUL Reply
what is sterilization
Sani
how can a doctor treat a person affected by endospore forming bacteria in his/her wound?
Mambo Reply
define disinfectant
Sani
the process of killing
shar
the process of killing microorganisms
shar

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Source:  OpenStax, Microbiology. OpenStax CNX. Nov 01, 2016 Download for free at http://cnx.org/content/col12087/1.4
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