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Express a small number in scientific notation (example) | Pre-Algebra | Khan Academy

Video vocabulary

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

count

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US / kaʊnt /

UK / kaʊnt /

A2
  • noun
  • Number of things added together, e.g. votes
  • With the number of crimes, knockouts, as stated
  • verb
  • To add things together to find the total number
  • To matter or be important
  • To include someone or something in a final number

exponent

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US / ɪkˈspəʊnənt /

UK / ɪkˈsponənt, ˈɛkˌsponənt /

C1
  • noun
  • Person who exemplifies an art movement, etc.

remember

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US / rɪ'membə(r) /

UK / rɪˈmɛmbɚ /

A1
  • verb
  • To give someone a gift, e.g. birthday, wedding
  • To hold a thought in your mind to not forget it
  • To bring a previous image or idea to your mind

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

keep

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US / ki:p /

UK / kip /

A1
  • noun
  • Large, strong tower in the middle of a castle
  • Money spent on you so you can live in a place
  • verb
  • To continue doing something; not to stop
  • To stop balls going in a goal in sports
  • To not give back or return something
  • (Of food) to not spoil or not rot
  • To take possession of something to own, e.g. a pet
  • To have and continue to hold something
  • To do something that you have promised or agreed
  • To stay in a certain place or condition
  • To maintain the rules

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

front

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US / frʌnt /

UK / frʌnt /

A1
  • adjecitve
  • Opposite of back; the forward part of an object
  • noun
  • Behavior not showing a person's true feelings
  • Area where fighting in a war is happening
  • Place where air of different temperatures meets
  • verb
  • To have the forward part facing something
  • To lead a group of people, usually a band

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

guess

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US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

many

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US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

ourselves

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US / ɑ:ˈselvz /

UK / aʊrˈsɛlvz, ɑr- /

A2
  • pronoun
  • (Showing speaker is affected by their own action)

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

scientific

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US / ˌsaɪənˈtɪfɪk /

UK / ˌsaɪənˈtɪfɪk /

A2
  • adjecitve
  • Concerning academic study of the physical world

small

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US / smɔ:l /

UK / smɔl /

A1
  • adjecitve
  • Little in size; not big
  • (Of letters) not written in capital letters
  • Being insignificant or minor
  • (Of a business) with few people or things; local
  • (Of voice) being soft and quiet
  • (Of a child) being young

shift

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US / ʃɪft /

UK / ʃɪft /

A2
  • adjecitve
  • (Of work) starting at a certain time, as at night
  • noun
  • A change in a persons plans, opinions or beliefs
  • Period of work starting at a certain time
  • verb
  • To change in position or direction
  • To move something from one place to another

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

equivalent

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US / ɪˈkwɪvələnt /

UK / ɪˈkwɪvələnt /

B1
  • adjecitve
  • Equal to something in value, use or meaning
  • noun
  • Thing like another in quality, quantity or degree

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

less

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US / les /

UK / lɛs /

A1
  • adjecitve
  • Smaller in amount or degree
  • adverb
  • To a smaller degree
  • noun
  • A smaller amount
  • preposition
  • With the subtraction of

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

fit

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US / fɪt /

UK / fɪt /

A2
  • adjecitve
  • Good looking; physically attractive
  • Proper or acceptable; morally or socially correct
  • noun
  • Sudden loss of body control; attack (of crying)
  • verb
  • To install a machine, equipment etc.
  • To adjust or change to the right size or shape
  • To be the right size and shape that you want

lead

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US / li:d /

UK / lid /

A1
  • adjecitve
  • Being the main part in movies or plays
  • noun
  • Wire for electricity, computer, etc.; cable
  • Information that could help to solve a crime
  • Main part in a play or movie
  • Heavy, gray metal element
  • Rope used to tie something to stop it escaping
  • Act of being at the front in a race or game
  • verb
  • To show the way or guide others
  • To be at the front of a race or game
  • To travel in front of; go in advance of others

natural

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US / ˈnætʃərəl /

UK / ˈnætʃərəl, ˈnætʃrəl /

A1
  • adjecitve
  • Being as one would expect; being usual or normal
  • Not made by humans; without human intervention

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

express

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US / ɪk'spres /

UK / ɪkˈsprɛs /

A1
  • adjecitve
  • Sent by a fast mail service
  • Traveling at high speed
  • noun
  • Fast train or bus
  • verb
  • To send something by fast mail
  • To state or show what you think or how you feel

start

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US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

decimal

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US / 'desɪml /

UK / ˈdɛsəməl /

B2
  • noun
  • Number using one equal tenth of a whole as a basis

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

definitely

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US / ˈdefɪnətli /

UK / ˈdefɪnətli /

A2
  • adverb
  • Without question; beyond doubt

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

good

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US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

zero

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US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

find

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US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

great

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US / ɡreɪt /

UK / ɡret /

A1
  • adjecitve
  • Very large in size
  • Very important
  • Very good; fantastic; wonderful
  • adverb
  • Very good; better than before
  • noun
  • Successful and well-admired person

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

bill

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US / bɪl /

UK / bɪl /

A2
  • noun
  • Plan for a new law being discussed by a government
  • Sign or poster advertising something
  • Paper money; a bank note
  • Piece of paper showing what you have to pay
  • Hard, often pointed part of a bird's mouth
  • Person's name
  • verb
  • To request payment by handing over an invoice

bunch

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US / bʌntʃ /

UK / bʌntʃ /

B1
  • noun
  • A group of things of the same kind
  • verb
  • To group people or things closely together
  • (Cloth) to gather/be gathered together in folds

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

tell

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US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

include

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US / ɪnˈklu:d /

UK / ɪnˈklud /

A1
  • verb
  • To make someone, something part of a group

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

step

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US / step /

UK / stɛp /

A1
  • noun
  • Movement done as part of a particular dance
  • Distance covered by one movement of a leg; stride
  • One part or stage in a process
  • Sound made by the feet while walking; footstep
  • Flat horizontal piece that forms stairs
  • verb
  • To raise and moving the foot to put it down

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

remind

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US / rɪ'maɪnd /

UK / rɪˈmaɪnd /

A2
  • verb
  • To cause someone to remember what they forgot

notation

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US / nəʊ'teɪʃn /

UK / noˈteʃən /

C2
  • noun
  • Set of written signs are used in music or math

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

skip

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US / skɪp /

UK / skɪp /

B2
  • noun
  • Very large waste disposal bin
  • verb
  • To move forward by taking fast steps and jumps
  • To not do something expected or required
  • To move rapidly, from one topic to another

example

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US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

essentially

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US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
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digit

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US / ˈdɪdʒɪt /

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B2
  • noun
  • Person's finger or toe
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general

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US / 'dʒenrəl /

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A1
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  • noun
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multiply

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B1
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rewrite

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A2
  • verb
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clearly

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A1
  • adverb
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between

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A1
  • preposition
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very

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US / 'verɪ /

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A1
  • adjecitve
  • Concerning a large degree or amount
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A1
  • noun
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A1
  • adverb
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all

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negative

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A2
  • adjecitve
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have

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raise

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  • noun
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  • Subtitles section
  • Express 0.0000000003457 in scientific notation.
  • So let's just remind ourselves what it means to be in scientific notation.
  • Scientific notation will be some number times some power of 10 where this number right here-- let me write it this way.
  • It's going to be greater than or equal to 1, and it's going to be less than 10.
  • So over here, what we want to put here is what that leading number is going to be.
  • And in general, you're going to look for the first non-zero digit.
  • And this is the number that you're going to want to start off with.
  • This is the only number you're going to want to put ahead of or I guess to the left of the decimal point.
  • So we could write 3.457, and it's going to be multiplied by 10 to something.
  • Now let's think about what we're going to have to multiply it by.
  • To go from 3.457 to this very, very small number, from 3.457, to get to this, you have to move the decimal to the left a bunch.
  • You have to add a bunch of zeroes to the left of the 3.
  • You have to keep moving the decimal over to the left.
  • To do that, we're essentially making the number much much, much smaller.
  • So we're not going to multiply it by a positive exponent of 10.
  • We're going to multiply it times a negative exponent of 10.
  • The equivalent is you're dividing by a positive exponent of 10.
  • And so the best way to think about it, when you move an exponent one to the left, you're dividing by 10, which is equivalent to multiplying by 10 to the negative 1 power.
  • Let me give you example here.
  • So if I have 1 times 10 is clearly just equal to 10.
  • 1 times 10 to the negative 1, that's equal to 1 times 1/10, which is equal to 1/10.
  • 1 times-- and let me actually write a decimal, which is equal to 0-- let me actually-- I skipped a step right there.
  • Let me add 1 times 10 to the 0, so we have something natural.
  • So this is one times 10 to the first.
  • One times 10 to the 0 is equal to 1 times 1, which is equal to 1.
  • 1 times 10 to the negative 1 is equal to 1/10, which is equal to 0.1.
  • If I do 1 times 10 to the negative 2, 10 to the negative 2 is 1 over 10 squared or 1/100.
  • So this is going to be 1/100, which is 0.01.
  • What's happening here?
  • When I raise it to a negative 1 power, I've essentially moved the decimal from to the right of the 1 to the left of the 1.
  • I've moved it from there to there.
  • When I raise it to the negative 2, I moved it two over to the left.
  • So how many times are we going to have to move it over to the left to get this number right over here?
  • So let's think about how many zeroes we have.
  • So we have to move it one time just to get in front of the 3.
  • And then we have to move it that many more times to get all of the zeroes in there so that we have to move it one time to get the 3.
  • So if we started here, we're going to move 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 times.
  • So this is going to be 3.457 times 10 to the negative 10 power.
  • Let me just rewrite it.
  • So 3.457 times 10 to the negative 10 power.
  • So in general, what you want to do is you want to find the first non-zero number here.
  • Remember, you want a number here that's between 1 and 10.
  • And it can be equal to 1, but it has to be less than 10.
  • 3.457 definitely fits that bill.
  • It's between 1 and 10.
  • And then you just want to count the leading zeroes between the decimal and that number and include the number because that tells you how many times you have to shift the decimal over to actually get this number up here.
  • And so we have to shift this decimal 10 times to the left to get this thing up here.