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Number Exponential Form Common Logarithm
1000 10 3 3
10 10 1 1
1 10 0 0
0.1 10 −1 −1
0.001 10 −3 −3

To find the common logarithm of most numbers, you will need to use the LOG button on a calculator.

Rounding and significant digits

In reporting numerical data obtained via measurements, we use only as many significant figures as the accuracy of the measurement warrants. For example, suppose a microbiologist using an automated cell counter determines that there are 525,341 bacterial cells in a one-liter sample of river water. However, she records the concentration as 525,000 cells per liter and uses this rounded number to estimate the number of cells that would likely be found in 10 liters of river water. In this instance, the last three digits of the measured quantity are not considered significant. They are rounded to account for variations in the number of cells that would likely occur if more samples were measured.

The importance of significant figures lies in their application to fundamental computation. In addition and subtraction, the sum or difference should contain as many digits to the right of the decimal as that in the least certain (indicated by underscoring in the following example) of the numbers used in the computation.

Suppose a microbiologist wishes to calculate the total mass of two samples of agar.

4.38 3 _ g 3.002 1 _ ______ g 7.38 5 _ g

The least certain of the two masses has three decimal places, so the sum must have three decimal places.

In multiplication and division, the product or quotient should contain no more digits than than in the factor containing the least number of significant figures. Suppose the microbiologist would like to calculate how much of a reagent would be present in 6.6 mL if the concentration is 0.638 g/mL.

0.63 8 _ g mL × 6. 6 _ mL = 4.1 g

Again, the answer has only one decimal place because this is the accuracy of the least accurate number in the calculation.

When rounding numbers, increase the retained digit by 1 if it is followed by a number larger than 5 (“round up”). Do not change the retained digit if the digits that follow are less than 5 (“round down”). If the retained digit is followed by 5, round up if the retained digit is odd, or round down if it is even (after rounding, the retained digit will thus always be even).

Generation time

It is possible to write an equation to calculate the cell numbers at any time if the number of starting cells and doubling time are known, as long as the cells are dividing at a constant rate. We define N 0 as the starting number of bacteria, the number at time t = 0. N i is the number of bacteria at time t = i , an arbitrary time in the future. Finally we will set j equal to the number of generations, or the number of times the cell population doubles during the time interval. Then we have,

N i = N 0 × 2 j

This equation is an expression of growth by binary fission.

In our example, N 0 = 4, the number of generations, j , is equal to 3 after 90 minutes because the generation time is 30 minutes. The number of cells can be estimated from the following equation:

N i = N 0 × 2 j N 90 = 4 × 2 3 N 90 = 4 × 8 = 32

The number of cells after 90 minutes is 32.

Most probable number

The table in [link] contains values used to calculate the most probable number example given in How Microbes Grow .

A table is titled Most Probable Number Table. For each row, it states the number of tubes giving a positive reaction for a 5-tube set for 10 mL, 1 mL and 0.1 mL tubes, followed by the MPN per 100 mL, and the 95% confidence limits for low and high. For row 1, the reactions are 10 mL = 0, 1 mL = 0, 0.1 mL = 0; the MPN is <2, and the low and high confidence limits are <1 and 7. For row 2, the reactions are 10 mL = 0, 1 mL = 1, 0.1 mL = 0; the MPN is 2, and the low and high confidence limits are <1 and 7. For row 3, the reactions are 10 mL = 0, 1 mL = 2, 0.1 mL = 0; the MPN is 4, and the low and high confidence limits are <1 and 11. For row 4, the reactions are 10 mL = 1, 1 mL = 0, 0.1 mL = 0; the MPN is 2, and the low and high confidence limits are <1 and 7. For row 5, the reactions are 10 mL = 1, 1 mL = 0, 0.1 mL = 1; the MPN is 4, and the low and high confidence limits are <1 and 11. For row 6, the reactions are 10 mL = 1, 1 mL = 1, 0.1 mL = 0; the MPN is 4, and the low and high confidence limits are <1 and 11. For row 7, the reactions are 10 mL = 1, 1 mL = 1, 0.1 mL = 1; the MPN is 6, and the low and high confidence limits are <1 and 15. For row 8, the reactions are 10 mL = 2, 1 mL = 0, 0.1 mL = 0; the MPN is 5, and the low and high confidence limits are <1 and 13. For row 9, the reactions are 10 mL = 2, 1 mL = 0, 0.1 mL = 1; the MPN is 7, and the low and high confidence limits are 1 and 17. For row 10, the reactions are 10 mL = 2, 1 mL = 1, 0.1 mL = 0; the MPN is 7, and the low and high confidence limits are 1 and 17. For row 11, the reactions are 10 mL = 2, 1 mL = 1, 0.1 mL = 1; the MPN is 9, and the low and high confidence limits are 2 and 21. For row 12, the reactions are 10 mL = 2, 1 mL = 2, 0.1 mL = 0; the MPN is 9, and the low and high confidence limits are 2 and 21. For row 13, the reactions are 10 mL = 2, 1 mL = 3, 0.1 mL = 0; the MPN is 12, and the low and high confidence limits are 3 and 28. For row 14, the reactions are 10 mL = 3, 1 mL = 0, 0.1 mL = 0; the MPN is 8, and the low and high confidence limits are 1 and 19. For row 15, the reactions are 10 mL = 3, 1 mL = 0, 0.1 mL = 1; the MPN is 11, and the low and high confidence limits are 2 and 25. For row 16, the reactions are 10 mL = 3, 1 mL = 1, 0.1 mL = 0; the MPN is 11, and the low and high confidence limits are 2 and 25. For row 17, the reactions are 10 mL = 3, 1 mL = 1, 0.1 mL = 1; the MPN is 14, and the low and high confidence limits are 4 and 34. For row 18, the reactions are 10 mL = 3, 1 mL = 2, 0.1 mL = 0; the MPN is 14, and the low and high confidence limits are 4 and 34. For row 19, the reactions are 10 mL = 3, 1 mL = 2, 0.1 mL = 1; the MPN is 17, and the low and high confidence limits are 5 and 46. For row 20, the reactions are 10 mL = 3, 1 mL = 3, 0.1 mL = 0; the MPN is 17, and the low and high confidence limits are 5 and 46. For row 21, the reactions are 10 mL = 4, 1 mL = 0, 0.1 mL = 0; the MPN is 13, and the low and high confidence limits are 3 and 31. For row 22, the reactions are 10 mL = 4, 1 mL = 0, 0.1 mL = 1; the MPN is 17, and the low and high confidence limits are 5 and 46. For row 23, the reactions are 10 mL = 4, 1 mL = 1, 0.1 mL = 0; the MPN is 17, and the low and high confidence limits are 5 and 46. For row 24, the reactions are 10 mL = 4, 1 mL = 1, 0.1 mL = 1; the MPN is 21, and the low and high confidence limits are 7 and 63. For row 25, the reactions are 10 mL = 4, 1 mL = 1, 0.1 mL = 2; the MPN is 26, and the low and high confidence limits are 9 and 78. For row 26, the reactions are 10 mL = 4, 1 mL = 2, 0.1 mL = 0; the MPN is 22, and the low and high confidence limits are 7 and 67. For row 27, the reactions are 10 mL = 4, 1 mL = 2, 0.1 mL = 1; the MPN is 26, and the low and high confidence limits are 9 and 80. For row 28, the reactions are 10 mL = 4, 1 mL = 3, 0.1 mL = 0; the MPN is 27, and the low and high confidence limits are 9 and 80. For row 29, the reactions are 10 mL = 4, 1 mL = 3, 0.1 mL = 1; the MPN is 33, and the low and high confidence limits are 11 and 93. For row 30, the reactions are 10 mL = 4, 1 mL = 4, 0.1 mL = 0; the MPN is 34, and the low and high confidence limits are 12 and 93. For row 31, the reactions are 10 mL = 5, 1 mL = 0, 0.1 mL = 0; the MPN is 23, and the low and high confidence limits are 7 and 70. For row 32, the reactions are 10 mL = 5, 1 mL = 0, 0.1 mL = 1; the MPN is 31, and the low and high confidence limits are 11 and 89. For row 33, the reactions are 10 mL = 5, 1 mL = 0, 0.1 mL = 2; the MPN is 43, and the low and high confidence limits are 15 and 110. For row 34, the reactions are 10 mL = 5, 1 mL = 1, 0.1 mL = 0; the MPN is 33, and the low and high confidence limits are 11 and 93. For row 35, the reactions are 10 mL = 5, 1 mL = 1, 0.1 mL = 1; the MPN is 46, and the low and high confidence limits are 16 and 120. For row 36, the reactions are 10 mL = 5, 1 mL = 1, 0.1 mL = 2; the MPN is 63, and the low and high confidence limits are 21 and 150. For row 37, the reactions are 10 mL = 5, 1 mL = 2, 0.1 mL = 0; the MPN is 49, and the low and high confidence limits are 17 and 130. For row 38, the reactions are 10 mL = 5, 1 mL = 2, 0.1 mL = 1; the MPN is 70, and the low and high confidence limits are 23 and 170. For row 39, the reactions are 10 mL = 5, 1 mL = 2, 0.1 mL = 2; the MPN is 94, and the low and high confidence limits are 28 and 220. For row 40, the reactions are 10 mL = 5, 1 mL = 3, 0.1 mL = 0; the MPN is 79, and the low and high confidence limits are 25 and 190. For row 41, the reactions are 10 mL = 5, 1 mL = 3, 0.1 mL = 1; the MPN is 110, and the low and high confidence limits are 31 and 250. For row 42, the reactions are 10 mL = 5, 1 mL = 3, 0.1 mL = 2; the MPN is 140, and the low and high confidence limits are 37 and 340. For row 43, the reactions are 10 mL = 5, 1 mL = 3, 0.1 mL = 3; the MPN is 180, and the low and high confidence limits are 44 and 500.

Questions & Answers

Differentiation between electron, proton and neutron
Zainab Reply
what are the roles of microorganisms in human being
Buhari Reply
some causes disease, others are not disease causing
Clark
they're necessary in our digestive system+the skin,everywhere actually the number of them in the human body alone is higher(by millions)than the number of humans cells,they're indispensable in the food industry,others are fundamental to make medicines and more,what exactly are you asking about ?
BENNINI
What are the natural occurring elements found in organisms on earth?
Otu Reply
some of the naturally occurring elements found in organisms are carbon, nitrogen, hydrogen, oxygen
Yashi
thanks
Mariam
some of them are carbon, oxygen, nitrogen, hydrogen, phosphorus and sulfur
Jamal
what is Zika virus?
Somali Reply
Zika virus is a mosquito-borne flavivirus that was first identified in Uganda in 1947 in monkeys. 
Cumar
intracellular vesicles are found in
Akshay Reply
how do i report widal slide results
Isaac Reply
how food can be used as a substrate for the growth of microorganisms
Ashi Reply
what is the importance of understanding chemistry in the field of microbiology and food technology?
Charmaine Reply
What is different between eukaryotes and prokcaryotic
Abia Reply
main difference is that eukaryotic cells possess membrane bound organelles
Iqra
prokaryotes are primitive organisms that doesn't contain membrane bound nucleus or any orgenelle while in eukaryotes membrane bound orgenelles and nucleus is present
Yashi
what s anatomy
jane Reply
its mean body structure, function, and systems
gazi
study of internal structure of living things
Falere
anatomy is the study structure of the made human
isir
anotomy is the actual study of body internally and externally Which include how itis made. for what and what is need of this
Iqra
la science anatomie c'est la science qui nous aide à étudier l'homme
Baraka
okay
Baraka
Ancestor are they real
Rapheal Reply
yes of course
David
yes please
Clark
50 50, depending on the accuracy of the clan records.
Vincent
okay
Baraka
Why protist is not a kingdom of Linnaeus 'S taxonomy?
Neha Reply
I dont know
Jeewraj
Linnaeus used Aristotle's criteria for dividing living organisms into kingdoms. Plants are immobile and insensitive, while animals are mobile and sensitive. the creatures he saw through the microscope were mobile, so he attributed them to animals.
Lad
name the different types of media use in lab to detect the micro organisms
Shehzadi Reply
The different types of media used in the lab to detect the microorganisms is known as cell culture..
Tean
solid media or broth is used to grow and detect microorganisms
Pohor
what is microbiology
Baraka
the study of large living organisms
Pratibha
the study of organisms which are micro in range
Vency
what is autoclaving?
Yashi
process for sterilization
Vency
is a machine used on the process of sterilisation
Clark
what is difference between hot air oven and autoclave as they both are used for sterilization ?
Vency
autoclave basically do moist heat sterilization while hot air oven do sterilization by dry heat.....
Yashi
what is the microbe
HUSSAIN
which method out of these two is best?
Yashi
why human have microbe
HUSSAIN
Hi
Sadam
hi to all
Sadam
depends on what to sterilize
Vency
microbes
Md
what is knowledge
HUSSAIN
well idea
Daniel
what are the importance of microbiologe to a nurse
Enny Reply
it enable a nurse to know the weight and height of a patient
Abotu
it helps the nurse in way as to give first aid to patient on which basis doctor will take diagonos
Iqra
disagree with both of you
Akhtar
ok
Abotu
Your Own idea
Abotu
it helps a nurse to be able to counsel a patient /client
Abotu
cell culture
Tean
Types of micro organisms
Jennifer Reply
Who discovered plant and animal cell
Jennifer
Robert Hooke
Martha

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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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