# 0.2 Mathematical basics

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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”):

${5}^{2}=5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}5=25$

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:

${5}^{3}=5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}5=125$

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:

${n}^{x}=n\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{n}^{x-1}$

## 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 $\frac{25}{100}$ , 3% means a ratio of $\frac{3}{100}$ , and 100 % percent means $\frac{100}{100}$ , 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.

$\text{25%}=\frac{25}{100}=\frac{1}{4}$

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.

$\text{10%}=\frac{10}{100}=0.10$

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.

$0.833=\frac{833}{1000}=\frac{83.3}{100}=83.3%$

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

$\frac{3}{4}=0.75=\frac{75}{100}=75%$

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.

$\frac{\text{carriers}}{\text{total students}}=\frac{15}{23}$

Then divide the numerator by the denominator.

$\frac{15}{23}=15÷23\approx 0.65$

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

$0.65\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100=65%$

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.

$\text{positive}+\text{negative}=9+28=37$

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

$\frac{\text{positive}}{\text{total students}}=\frac{9}{37}$

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

$\begin{array}{c}\frac{9}{37}=9÷37\approx 0.24\hfill \\ 0.24\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100=24%\hfill \end{array}$

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:

$\frac{9}{37}=\frac{x}{100}$

Now, cross multiply and solve for the unknown:

introduction to microbiology
Study the life of microorganisms present in the environment their survivals etc..
ayesha
Microscopic organisms, commonly known as microorganisms or microbes, are found all around us and even inside our bodies. The category 'Microbes' includes a massive range of organisms including bacteria, fungi, viruses, algae, archaea and protozoa.
Amre
fermented foods likely benefited ancestors to preserve foods and make other foods like milk, cheese, and bread using microbes.
the evidence that I would support the statement regarding ancient people ideas that disease was transmitted by things they could not see is by the discoveries under a microscope. Many microbiologists have discovered certain diseases caused by microbes.
Zinnia
plz give the information about glyoxylate cycle
what type of information?
Sapiens
I need medical microbiology mcqs books for Mbbs
Kisota
for pakistani mbbs or other?
Sapiens
what is microbial soup?
😃😂funny question isn't it?!!! sorry for inconvenience 😊
ayesha
most bacterial pathogens that cause disease in humans are classified in terms if their preferable ph as
what is micro
extremely small in size
Swetha
almost invisible to the naked eye
Peter
thanks
uwc
Peter
invisible sized objects
Sivasri
invisible sized object or specimens.which is used to see in only the microscope that specimens or objective called the micro
Sivasri
small organism that can be seen by use of Microbes
Manyang
why do you need to study microorganisms
Sala
what is microbiology?
microbiology is a branch of biology .it deals with the study of microorganisms life cycle , uses, disadvantages,and it impact in any other fields .which is used to view in microscope .
Sivasri
Microbiology is the study of microorganisms, those being unicellular, multicellular, or acellular. Microbiology encompasses numerous sub-disciplines including virology, bacteriology, protistology, mycology, immunology and parasitology.
Raj
In short , it is the study of micro organisms and types , characteristics.
Kaviya
can you explain the structure of rna in detail
RNA is of many types....like mRNA,tRNA,rRNA,snRNA,guideRNA..etc .
Swetha
but generally RNA is single stranded
Swetha
It contains adenine guanine cytosine , instead of thymine it contains uracil.
Swetha
ribonucleic acid present in RNA.. where as in DNA it is deoxyribonucleic acid...and ribonucleotide is present in RNA
Swetha
RNA is a blue print of DNA. it has the information from DNA....and we can predict the base panirs in DNA if we have the RNA....copy of that DNA
Swetha
can either have positive or negative polarity
Ernestine
Diatoms need..... With the help of which they can construct their beautiful cell wall
Microbial growth curve shows a.... Curve.
diminishing curve
Oluwapamilerin
It represents the decreasing growth of an organism.
Swetha
what is meant by reverse isolation in tuberculosis treatment?
why do we study microbiology
Microbiology is the way of gaining knowledge about those organisms which are surround us but we can't see them with our naked eye,such organisms called microorganisms..We can see them only under microscope.
ayesha
from our birth to death microorganisms are with us in the environment as well as on our body which are called Microflora.
ayesha
Microfloras are non pathogenic
ayesha
what is microbiology
It is the study of microorganisms and their structures functions and their interactions with environment ...
Swetha
it is the study of microorganisms which are invisible to backed eye but we can see them under microscope then microbiology is the study of microorganisms including their structures , functions,and their interactions with environment
Swetha
tq
Anji
tqq...not backed eye sorry nacked eye
Swetha
it's ok
Anji
where r u from
Anji
thank you
Swetha
from India
Swetha
which state
Anji
Swetha
Anji
chelusu nakku kochum
Swetha
thank you
Swetha
what is reverse isolation in tuberculosis treatment?
Swetha
Reverse isolation is used to protect you from germs when your immune system is not working properly. Germs can be carried on droplets in the air, medical equipment, or another person's body or clothing.
Kaviya
will you repeat this again?
Swetha
Reverse isolationis used to protect you from germs when your immune system is not working properly. Germs can be carried on droplets in the air, medical equipment, or another person's body or clothing.
Kaviya
kill you?
Swetha
Y
Kaviya
nothing to see the whole answer that is why I sent u like that then only I can see the full answer la
Swetha
What is allosteric site?
I don't know how to explain but it's a deep concave site of an enzyme it's slightly or more slightly similar to the active site on an enzyme
ayesha
a site other than enzyme active site
describe the gram staining procedure as used in identification and classification of bacteria and it's interpretation
Gram staining method found by Hans Christian Gram. Classified into Gram Positive and Gram Negative Positive would be purple or blue stained bacteria Negative would be Pink or Red stained bacteria Both are observed under microscope This procedure performed on glass slides by making a smear of sample.
ayesha
Thanks.. nicely u defined
shamim
jazakallah Khair
ayesha
hmmm
shamim
Masha allah
Khamis
jazakallah Khair
ayesha
hi
Nafiu

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