# 1.1 The scope and scale of physics  (Page 4/12)

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## Order of magnitude

The order of magnitude    of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude refers to the scale (or size) of a value. Each power of 10 represents a different order of magnitude. For example, ${10}^{1},{10}^{2},{10}^{3},$ and so forth, are all different orders of magnitude, as are ${10}^{0}=1,{10}^{-1},{10}^{-2},$ and ${10}^{-3}.$ To find the order of magnitude of a number, take the base-10 logarithm of the number and round it to the nearest integer, then the order of magnitude of the number is simply the resulting power of 10. For example, the order of magnitude of 800 is 10 3 because ${\text{log}}_{10}800\approx 2.903,$ which rounds to 3. Similarly, the order of magnitude of 450 is 10 3 because ${\text{log}}_{10}450\approx 2.653,$ which rounds to 3 as well. Thus, we say the numbers 800 and 450 are of the same order of magnitude: 10 3 . However, the order of magnitude of 250 is 10 2 because ${\text{log}}_{10}250\approx 2.397,$ which rounds to 2.

An equivalent but quicker way to find the order of magnitude of a number is first to write it in scientific notation and then check to see whether the first factor is greater than or less than $\sqrt{10}={10}^{0.5}\approx 3.$ The idea is that $\sqrt{10}={10}^{0.5}$ is halfway between $1={10}^{0}$ and $10={10}^{1}$ on a log base-10 scale. Thus, if the first factor is less than $\sqrt{10},$ then we round it down to 1 and the order of magnitude is simply whatever power of 10 is required to write the number in scientific notation. On the other hand, if the first factor is greater than $\sqrt{10},$ then we round it up to 10 and the order of magnitude is one power of 10 higher than the power needed to write the number in scientific notation. For example, the number 800 can be written in scientific notation as $8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}.$ Because 8 is bigger than $\sqrt{10}\approx 3,$ we say the order of magnitude of 800 is ${10}^{2+1}={10}^{3}.$ The number 450 can be written as $4.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2},$ so its order of magnitude is also 10 3 because 4.5 is greater than 3. However, 250 written in scientific notation is $2.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}$ and 2.5 is less than 3, so its order of magnitude is ${10}^{2}.$

The order of magnitude of a number is designed to be a ballpark estimate for the scale (or size) of its value. It is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math with very big and very small numbers easier. For example, the diameter of a hydrogen atom is on the order of 10 −10 m, whereas the diameter of the Sun is on the order of 10 9 m, so it would take roughly ${10}^{9}\text{/}{10}^{-10}={10}^{19}$ hydrogen atoms to stretch across the diameter of the Sun. This is much easier to do in your head than using the more precise values of $1.06\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-10}\text{m}$ for a hydrogen atom diameter and $1.39\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\text{m}$ for the Sun’s diameter, to find that it would take $1.31\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{19}$ hydrogen atoms to stretch across the Sun’s diameter. In addition to being easier, the rough estimate is also nearly as informative as the precise calculation.

## Known ranges of length, mass, and time

The vastness of the universe and the breadth over which physics applies are illustrated by the wide range of examples of known lengths, masses, and times (given as orders of magnitude) in [link] . Examining this table will give you a feeling for the range of possible topics in physics and numerical values. A good way to appreciate the vastness of the ranges of values in [link] is to try to answer some simple comparative questions, such as the following:

#### Questions & Answers

What is action of point ?
Bishal Reply
a point . is the spot and the action is what u do when ur at the spot . but the action of a point idk a divider
Darth
Quantity which are used in physics simply
Sangram Reply
That's philosophical question.
Jan
What is the Physical quantity
Raja Reply
What is Centripetal force
Taiwo Reply
a force of attraction that tends to keep a body moving in a circular path
Mustapha
force pulling the particle towards the center when moving in circular path
juny
yes
Mustapha
good job
Pranshu
y oxygen is shift to first place
Radhika Reply
What is coriolis firce
Shakeel Reply
Angular accelaration force,as the result of the rotatation of earth
Arzoodan
Due to the rotation of the earth the winds at the equator get deflected in opposite direction and therefore cause some currents in the Northern and Southern hemisphere which are opposite in there spin.
Varsha
Thats correct.
Arzoodan
if cos = x/y then sec = y/x if sin = y/x then cosec = x/y
Jan Reply
if cosβ=x/y then what is cosecβ
Abubakar Reply
. if cosβ=x/y what is cosecβ
Abubakar
if cosΦ=x/y what is cosecΦ
Abubakar
What are the unknown symbols?
Jan
Î²
Jan
Î¦
Jan
It is defined that cosec = 1/sin and sec = 1/cos
Jan
Do you understand this?
Jan
of cours
Arzoodan
∇(f/g) = (g∇f − f∇g)/g^2 , at points x where g(x) 6= 0 please help me to solve the problem ....
11 Reply
sir please add answer sheet of spigel vector analysis ..
11 Reply
In a pulley system 2 boxes r hanging in both sides of pulley. An other box was joined to the left box through a rope & get accelerated downward. If all the boxes have same mass ,then what will be the acceleration of that system ?
bibek Reply
it may be mg
Amalesh
∇(f/g) = (g∇f − f∇g)/g2 , at points x where g(x) 6= 0 plus solve it
11
What is momentum
Rika Reply
is the product of mass to it's velocity (mv)
Ahmed
momentum
oladipupo
quatity of motion present in a body or product of mass and velocity
Shakeel
show that the kE of a uniform ring of mass m rolling along a smooth horizontal surface so that its centre of mass has a velocity v is mv×v
folder
what is hydration energy
osobase Reply
the energy................................................
Rika
what is momentum
Ogwu Reply
dont know want to know the answer
Rika
it's the product of mass multiplied by velocity
harsha
the quantity of motion possessed by a body is called its momentum.by virtue of which a body can exert a force in the agency which tend to stop it .it is a common experience that stronger force is required to stop more massive body.also faster the body moves harder it is to stop it .this is why
Manoj
momentum is product of mass and velocity and it is denoted by "P".
Manoj
show that the cross product of vector axb=-bxa
Teklu Reply

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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