# 0.3 Exponents  (Page 2/4)

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$N=\text{602},\text{300},\text{000},\text{000},\text{000},\text{000},\text{000},\text{000}$

Question: How can Avogadro’s number be expressed in scientific notation?

Solution: Avogadro’s number can be written as the product of a real number (6.023) by the term (100,000,000,000,000,000,000,000)

$N=6\text{.}\text{023}×\text{100},\text{000},\text{000},\text{000},\text{000},\text{000},\text{000},\text{000}$
$N=6\text{.}\text{023}×{\text{10}}^{\text{23}}$

Rather than trying to perform calculations using the decimal form for Avogadro’s number, chemists have learned to appreciate the more mathematically tractable scientific notation form of this important constant.

Engineering notation is quite similar to scientific notation. Numbers are written in engineering notation in the following form

$a×{\text{10}}^{c}$

where the coefficient a is a real number in the range 1<| a |<1,000 and the exponent c is restricted to be an integer multiple of 3.

An additional restriction on the coefficient ( a ) requires that a be expressed using no more than 3 significant digits. The restriction that the exponent be an integer multiple of 3 allows the numbers that result from the transformation to engineering notation to be expressed using the standard prefixes associated with the Scientifique Internationale (SI) system of units.

Example (Width of the Asteroid Belt)

Let’s consider the following application of engineering notation. The width of the asteroid belt has been determined to be 280,000,000 m .

Question: What is the width of the asteroid belt expressed in engineering notation?

Solution: Let us begin by expressing this quantity using scientific notation

$\text{280},\text{000},\text{000}m=2\text{.}\text{80}×{\text{10}}^{8}m$

We notice that the exponent is not an integer multiple of 3, so this quantity is not yet expressed in engineering notation. We do know that

${\text{10}}^{8}={\text{10}}^{2+6}={\text{10}}^{2}×{\text{10}}^{6}$

This quantity can be substituted into the previous equation to yield the expression for the width of the asteroid belt in engineering notation

$\text{280},\text{000},\text{000}m=2\text{.}\text{80}×{\text{10}}^{8}m$
$\text{280},\text{000},\text{000}m=2\text{.}\text{80}×{\text{10}}^{2}×{\text{10}}^{6}m$
$\text{280},\text{000},\text{000}m=\left(2\text{.}\text{80}×\text{100}\right)×{\text{10}}^{6}m$
$\text{280},\text{000},\text{000}m=\text{280}×{\text{10}}^{6}m$
$\text{280},\text{000},\text{000}m=\text{280}\text{Mm}$

## Application: electrical power

We will begin our investigation of applications of exponents with a discussion of electrical power. Consider the electrical circuit diagram that shows a source voltage ( V ) attached to a resistor ( R ) to produce a current ( I ).

The relationship between V, R and I is summarized by Ohm’s Law

$V=I×R$

where V is measured in volts (V) , I is measured in amps (A), and R is measured in ohms (Ω).

We may write an expression for the current as

$I=\frac{V}{R}$

The power that is absorbed by the resistor is known to be the product of the current flowing through the resistor time the potential difference (voltage) across the terminals of the resistor. If we denote the power absorbed by the resistor as P R , then it can be expressed mathematically as

${P}_{R}=I×V$

Substitution of the expression for I obtained from Ohm’s Law yields an equivalent expression for the power absorbed by the resistor

${P}_{R}=\left(\frac{V}{R}\right)\cdot V=\frac{{V}^{2}}{R}$

Paying attention to the exponent, we can say that the power absorbed by the resistor is the square of the voltage across the terminals of the resistor divided by the resistance. The units associated with power are Watts (W).

#### Questions & Answers

can someone help me with some logarithmic and exponential equations.
sure. what is your question?
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
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Cesar
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preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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