# 1.2 Units and standards  (Page 5/17)

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Check Your Understanding Restate $4.79\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\text{kg}$ using a metric prefix such that the resulting number is bigger than one but less than 1000.

$4.79\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}$ Mg or 479 Mg

## Summary

• Systems of units are built up from a small number of base units, which are defined by accurate and precise measurements of conventionally chosen base quantities. Other units are then derived as algebraic combinations of the base units.
• Two commonly used systems of units are English units and SI units. All scientists and most of the other people in the world use SI, whereas nonscientists in the United States still tend to use English units.
• The SI base units of length, mass, and time are the meter (m), kilogram (kg), and second (s), respectively.
• SI units are a metric system of units, meaning values can be calculated by factors of 10. Metric prefixes may be used with metric units to scale the base units to sizes appropriate for almost any application.

## Conceptual questions

Identify some advantages of metric units.

Conversions between units require factors of 10 only, which simplifies calculations. Also, the same basic units can be scaled up or down using metric prefixes to sizes appropriate for the problem at hand.

What are the SI base units of length, mass, and time?

What is the difference between a base unit and a derived unit? (b) What is the difference between a base quantity and a derived quantity? (c) What is the difference between a base quantity and a base unit?

a. Base units are defined by a particular process of measuring a base quantity whereas derived units are defined as algebraic combinations of base units. b. A base quantity is chosen by convention and practical considerations. Derived quantities are expressed as algebraic combinations of base quantities. c. A base unit is a standard for expressing the measurement of a base quantity within a particular system of units. So, a measurement of a base quantity could be expressed in terms of a base unit in any system of units using the same base quantities. For example, length is a base quantity in both SI and the English system, but the meter is a base unit in the SI system only.

For each of the following scenarios, refer to [link] and [link] to determine which metric prefix on the meter is most appropriate for each of the following scenarios. (a) You want to tabulate the mean distance from the Sun for each planet in the solar system. (b) You want to compare the sizes of some common viruses to design a mechanical filter capable of blocking the pathogenic ones. (c) You want to list the diameters of all the elements on the periodic table. (d) You want to list the distances to all the stars that have now received any radio broadcasts sent from Earth 10 years ago.

## Problems

The following times are given using metric prefixes on the base SI unit of time: the second. Rewrite them in scientific notation without the prefix. For example, 47 Ts would be rewritten as $4.7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{13}\text{s.}$ (a) 980 Ps; (b) 980 fs; (c) 17 ns; (d) $577\phantom{\rule{0.2em}{0ex}}\mu \text{s}.$

The following times are given in seconds. Use metric prefixes to rewrite them so the numerical value is greater than one but less than 1000. For example, $7.9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\text{s}$ could be written as either 7.9 cs or 79 ms. (a) $9.57\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\text{s;}$ (b) 0.045 s; (c) $5.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\text{s;}$ (d) $3.16\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\text{s.}$

a. 957 ks; b. 4.5 cs or 45 ms; c. 550 ns; d. 31.6 Ms

The following lengths are given using metric prefixes on the base SI unit of length: the meter. Rewrite them in scientific notation without the prefix. For example, 4.2 Pm would be rewritten as $4.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{15}\text{m.}$ (a) 89 Tm; (b) 89 pm; (c) 711 mm; (d) $0.45\phantom{\rule{0.2em}{0ex}}\mu \text{m}\text{.}$

The following lengths are given in meters. Use metric prefixes to rewrite them so the numerical value is bigger than one but less than 1000. For example, $7.9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\text{m}$ could be written either as 7.9 cm or 79 mm. (a) $7.59\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\text{m;}$ (b) 0.0074 m; (c) $8.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\text{m;}$ (d) $1.63\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{13}\text{m.}$

a. 75.9 Mm; b. 7.4 mm; c. 88 pm; d. 16.3 Tm

The following masses are written using metric prefixes on the gram. Rewrite them in scientific notation in terms of the SI base unit of mass: the kilogram. For example, 40 Mg would be written as $4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\text{kg.}$ (a) 23 mg; (b) 320 Tg; (c) 42 ng; (d) 7 g; (e) 9 Pg.

The following masses are given in kilograms. Use metric prefixes on the gram to rewrite them so the numerical value is bigger than one but less than 1000. For example, $7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{kg}$ could be written as 70 cg or 700 mg. (a) $3.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\text{kg;}$ (b) $2.3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{17}\text{kg;}$ (c) $2.4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\text{kg;}$ (d) $8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{15}\text{kg;}$ (e) $4.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\text{kg.}$

a. 3.8 cg or 38 mg; b. 230 Eg; c. 24 ng; d. 8 Eg e. 4.2 g

who discover periodic table?
it wasn't discovered , it was made.and the person who made it was dmitri mendeleev. dobreinier and newland gave their laws before dmitri related periodic table but wasn't successful in their work
Ritik
Nope, numerous number of scientist had actually contributed in the making of periodic table. Dmitri Mendeleev succeeded making all the elements into the right order in accordance to their atomic number.
Dame
what is the Greek name for calcium
different types of wave
longitudinal and transverse waves
Ravindra
a gun is kept in the state that it cannot move anywhere and the bullet is fired. Then what is the effect on the velocity of bullet and KE of gun ?
want is meant by the term solar system
it refers to the sun and all heavenly bodies revolving around it.
Danie
excatly...for sure
Arzoodan
in addition to Danie's, a solar system is a collection of planets and their moons, asteroids, and other objects bound together by the Star's gravitational force directly or indirectly.
Galiwango
what is meant by total internal reflection
what iw meant by total internal reflection
Akshay
Lorentz force?
jyotirmayee
study fibre optics. .you will get total internal reflection
Siddhansh
wha
jyotirmayee
what is Lorentz force?
jyotirmayee
a ray of light traveling at an angle of incidence greater than critical angle from denser to rarer medium is totally reflected back into the denser medium is called total internal reflaction
Manoj
motion in strat line where is this chapter
what is Lorentz force?
what is maxwell electromagnetic law?
jyotirmayee
at what angle should the two forces 2p and root 2p acts so that the resultant force is p root 10
Akshay
what's the working difference between a dynamo and a pump?
a dynamo is basically a dc generator while pump is usually equipped with a motor
vedanth
a dynamo converts mechanical energy to electrical while a pump is opposite to that
vedanth
nice
Piyali
okay
Friday
why sea water looks bluish?
cuz the sky is blue...
Mehdi
you see the reflexion of the "blue" sky in the water
Mehdi
somewhere sea water turns green why?
Piyali
never seen bro... are u sure ?
Mehdi
ur answer was correct but due to the presence of phytoplankton color can be changed near the shore
Piyali
waaaww... you re awesome
Mehdi
because of the reflection of the sky
Friday
rays coming from the sun consist of all 7 colours ie.VIBGYOR. when the ray strikes surface of water,all colors gets absorbed by it except blue which gets reflected by it.so we find the sea water appearing bluish
Ritik
how can someone identify sea water from rain water
Oniyide
i think it's not possible as because rainwater consists of water from all kind of water bodies ie.lakes,seas etc but u can predict if u have a sea nearby ur home or city
Ritik
i need solutions of unuversity pbysucs volume 1
me too
Nirupam
Help us if anyone knows
Nirupam
bring questions
john
actually if u wanted whole book solution then u should buy the solution book
jyotirmayee
from where
Nirupam
where do u live ,,,,,if u live in Delhi then at bellsarayeiii or from stationary store ,,,,chatarpurrr ,,,,,there is a popular books store,,,,,u have to buy from there
jyotirmayee
Kota Rajasthan
Nirupam
so strange,,,,,r u preparing for pmt,,,?
jyotirmayee
for IIT
Nirupam
then concern near book store
jyotirmayee
in Rajasthan
jyotirmayee
jyotirmayee
Nirupam
its fine,,most welcome
jyotirmayee
what is three dimensional coordinate system?
considering the change of vectors in all three dimensions of space
vedanth
direction co-sign of vector questions
opposite
Sonu
opposite mean
Vipin
what is the different between action and reaction?
action is external force. Reaction exists because of the external action. Reaction is mostly an internal force
Yoblaze
The difference is said in the word itself. There is no existance of reaction without an application of action. So action occur first then reaction. Reaction may produce in body itself or to other body i.e., it may be internal or external.
Amalesh
or we can say , reaction is the result of action
Ritik