# 0.2 Mathematical basics

 Page 1 / 3

## 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:

write the life cycle of HIV
describe the internal and external structure of prokaryotic cell in terms of there appearance and functions
compare and contrast similar structures found in prokaryotic and eukaryotic cells
Lenia
control of microorganisms
how can a doctor treat a person affected by endospore forming bacteria in his/her wound?
a 28 years old woman come to your clinic with complain of fever painful genital blisters which express clear fluid when ruptured burning sensation around the bristers what is the diagnosis?
genital herpes caused by a virus called herpe simplex virus
Doris
what is the reference between selective medium and differential medium?
the micro flora of air is transient why
Princess
Hello.... Am new here
welcome essien
welcome essien
Beka
classification of gram positive
classify gram positive
lissa
catalase test is done to differentiate between staph and strep. as staph is catalase positive while strep is catalase negative then staph is differentiate further on coagulase positive and coagulase negative. staph aureus is coagulase positive while staph epidermidis is coagulase negative.
gram positive staph is further differentiated on sensitivity test and manitol salt fermentation test while gram positive strep is differentiated on hemolysis pattern
lissa
lissa
ok
Blessing
am back any gist
Blessing
taxonomy
Rahul
can i use the graph of bacterial growth for my master's thesis?
facultative anaerobic bavteria gives uniform turdibity in nutrient broth why?
oils and waxes are not sterilized in autoclave
Princess
what is the function of paraffin
@ MAHI because they can grow all over the media from surface to the bottom as they can utilize oxygen or conduct fermentation in its absence.
Online
2.@MAHI Autoclave uses steam under pressure. The steam cannot penetrate through oil and wax. Thus, dry heat sterilization is preferred than autoclave .
Online
thnku
how nutirent agar can converted into blood agar
Princess
thank you
Princess
take a nutrient agar ........and add 5ml blood and put in it ...........!
nutrient agar +blood 5ml+ distilled water =blood agar .
mixed wellllll
hi
Rahul
why agar is not a neutrient source?
Shimul
because it's a general purpose agar only use for growing bacteria
Richa
way is antigen
opaleye
what is antigen
opaleye
antigen is a foreign body that cause activation of antibody?
ASNAKE
Antigen is a toxin or other foreign substance which induces an immune response in the body, especially the production of antibodies.
Shimul
thanks for that
opaleye
what is pharmacology
Luyenu
a science that studies about the drug
ASNAKE
hello ever one
Sayid
y
Abdul
Work hard
Anigor
y
Abdul
thanks alot
Luyenu
What is the major different between gram positive and gram negative bacteria.
Asikur
bacteria kya hai
Mala
content of their cell wall
Doris
koi mujhse basic microbiology ki study k Lea book suggest kro .
Richa
Harley prescott
Vikas
what are the five predisposing factors of opportunistic infections
1. long term exposure to diseases, that the body immunity weakens.
prosper
2. Nature Of some diseases to weaken body immunity such as, AIDS.
prosper
3. Use of immuno-suppresive drugs.
prosper
anyone... need a hand here 🙋😞
prosper
Low immune is the major cause eg for kaposis sarcoma
Davismith
suitable conditions e.g temp,
what os gnormal flora
morphological and genetic classification of bacteria
what is the morphogical
Bupe
h
Sudhir
morphologycal is defined as relating to the branch of biology that deals with the form of living organisms,and with relationship between their structures.
relating to the form or structure of things .
what is the meaning of lessions
oluwa
i am frim Afghanistan.
iam from iraq
Haidar
and i'm from pakistan
Nice
Amina
Hlo
Asiya
Hmm
Number
Mujtafa
am ustaz Abdulsalam from Ghana
ustaz
am Bupe Chifita from Zambia
Bupe
what is microbiology
Bupe
is the study of invisible micro organism
Mujtafa
microbiology is the study of very too small organisms which we can't see with naked eyes ......in other words ....study of microorganism is called microbiology.
Hello! How Can Microorganisms Be Isolated From The Skin?.. 5 ways if possible. (briefly)
prosper
from skin swabbing is the prefer method worldwide
prosper
hi
Meek
hi Meek
prosper
are there any other ways pals?
prosper
hi prosper
Meek
hello Meek Mild.
prosper
Any question or ideas, Meek?😊
prosper
and if a patient have any blister or abscess on the skin then first cut the blister or abscess. inside material is taking by syringe.
in case of fingernail or toenails simply cut a small piece of nail and culture on the appropriate media at a required temperature and time
Again, thanks Mr. Muhammad! I appreciate the help.
prosper
you welcom prosper 😊
what are the media use for skin swab?
Sieh-Mlanwin
blood and macckonkey mostly usededia for skin bacteria
used media*
@ SIEH mostly fungal infection occurs in skin so SDA ( Sabouraud Dextrose Agar) or MEA ( Malt extract agar) are common.
Online
thanks
Sieh-Mlanwin
Microbiologicam source of vitamins
what do you mean?
Md
that's example?
Md
hi everyone
such as. c/s media
Md
hmm hlw
Md
just tell me about that ?
Md
where are u from