# 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:

what z microbiology
what happened when someone died and what happened to the blood
nice question
Attari
when you die you have no memory and the blood dry off
Falere
Ridwan
And how many does the microorganisms is classified?
Ridwan
what is endoparasites and exo parasite and their example
Endo : inside the body Exo/ecto : outside or on the body
Paul
OGEDE
Louse for exo/ecto Helminths (worms) for endo
Paul
what's prokaryotic
A prokaryotic cell is a cell with no membrane bounds organelles
Paul
what are the main effect of parasite?
nutritional group of micro organism
what are the charateristic bacteria, eukaryotes, and viruses have in commom
D N A ar purno rup ki
বাংলায় দেখবো DNA এর পূর্রন্যরুপ কি
Ruba
what's microbiology
micah
micro biology is the study of micro organisms,those being unicellular multicellular or a cellular
aniisha
deoxyribonucleic acid is a long molecule that contains our unique genetic code.
aniisha
Does the parasite/parasitology are under microbiology or not
yunusa
Define bacteria
Kainat
Bacteria are a type of biological cell & they constitute a large domain of prokaryotic microorganisms.
raisa
what kind of microbiology
Mira
hello what is main function of T and B cells
T cells are involved in cell-mediated immunity while B cells are primarily responsible for humoral immunity (relating to antibodies)
Janet
what is hepatitis B
Sunday
it's viral infection that attacks the liver and can cause both acute and chronic diseases. the virus is most commonly transmitted from mother to child during birth and delivery, as well as through contact with blood or other body fluids...
Dejene
What are fundamental experiment of microbiology?
study of microscopic organisms, unicellular and multicellular
Falere
what are the characteristics of bacteria, viruses, and eukaryotes
Ami
bacteria-are living organism. contain a peptidoglycan/lipopolysaccharide cell wall. VIRUS-are considered as organic structure which interact with living organism don't have acell wall. they have many differents like bacteria size -large(1000nm) virus size-smaller(20-400nm). bacteria ribosomes presen
Dejene
virus ribosomes absence. bacteria living organism. virus b/n living and non-living things
Dejene
eukaryotic cell has a true membrane bond nucleus and has other membranous organelles that allow for compartmenalization of function
Dejene
who discovered the growth curve
Example of coccus bacteria
staphylococcus aureus
Elton
MRSA any bew information
Satish
Satish
Any stru tural finding about novel corona virus
Satish
Examples of spiral bacteria
Example of Bacillus bacteria
Nweke
pusals
manikanta
another one
Nweke
what is the desifection decontamination or sterilization
Is the removal of dangerous substances or germs from an area, objects or person
Florence
It is the removal of any pathogen, including their spores
Paul
removal of all forms of life including endospore
abdulbasid
I think there is a difference between disinfection and sterilization... we should consider those....
Mosimanegape
disinfection deals with removing harmful microbes at the surface level it doesn't destroy or kill spores ( it uses oxidizing agents ,alcohols , phenolic comp ,aldehydes etc) but sterilization deals with total elimination of all forms of lives.(this uses heat, steam, radiation and chemicals)
Onyinye
disinfecting is preventing microorganisms while sterilization is killing of microorganisms completely
Janet  By By By By By Rhodes By   