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Scientific Notation - Fast Review!

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in this lesson i want to give you a

basic introduction into scientific notation

notation

scientific notation is a useful way to

represent very large numbers or very

small numbers so

let's say if we have the number forty

five thousand

how can we express this number in

scientific notation

now you want to move the decimal

in between the first two numbers that is

between the four and five

so i'm going to move it four units to

the left one

two three four

so forty five thousand

is equal to four point five times ten to

the four

now it's important to understand that if

this number is positive

it's associated with a very large number

if this is a negative exponent it will

be associated with a very small number a

number between 0 and 1.

so let's work on some more examples

try these two examples

actually maybe more than two let's say

thirty seven fifty

9.3 billion

go ahead and convert these numbers

into scientific notation

feel free to pause the video

so let's start with this one

i'm gonna put the decimal between a

three and a seven so this is one two three

three

since i moved it three spaces to the

left this is going to be 3.75

times 10 to the third power

and that's pretty straightforward

now let's move on to the next one

so i want the decimal point

to be between the 5 and the 8

so i'm going to move it 1 2 3 4

five units to the left

so therefore this is going to be 5.8

times 10 to the 5.

now for the next example

i want it to be between a 7 and a 2.

so this is going to be this is 3

6 and then 7.

so i move this 7 space to the left so

it's going to be 7.2 times 10 to the 7

and that's it for that one now for the

last one

i'm going to start here 3

3 6

9 units to the left

so this is going to be 9.3

times 10 to the ninth power

and that's a simple way to express very

large numbers using scientific notation

now what about some small numbers

we still want the decimal to be between

the two and a three

but this time i'm going to move it to

the right as opposed to the left

so i need to move it three spaces

to the right so therefore this is going

to be 2.3

times 10 to the negative 3.

now keep in mind a negative exponent

will always be associated with very

small numbers

a positive exponent will be associated

here's some more examples that you can try

so go ahead and try those examples

so this is three

four units so this is going to be 7.6

times 10 to the negative 4.

so anytime you have these decimal values

it's going to have a negative exponent

associated with the scientific notation number

number

so for this one i've got to move it two

units to the right

and so that's going to be four point nine

nine

times ten to the minus two

now for the third example this is three six

six seven

seven

actually not that far i needed to be

between the first two numbers so three

and six

so this is going to be five point four one

one

this is 3 6

9 and then 10 units to the right

so this is going to equal 8.35

times 10 to the negative 10.

and so now you know how to convert

a number in decimal notation or standard notation

notation

now let's switch it up a bit let's work

on converting

a number from scientific notation

standard notation

so let's say if we have 2.4 times 10 to

what is this

now keep in mind that we said that if we

have a positive exponent it will be

associated with a larger number

so we need to increase the value of 2.4

so should we move the decimal to the

right or to the left

to increase the value we need to move it

to the right so we have the number 2.4

and let's add some zeros to it

so we're going to move it two units to

the right

so therefore this is going to change

to 240

and that's the answer

now if you think about what this

expression means

10 squared that's 10 times 10 which is 100

100

so this really means 2.4 times 100

which is 240. and so you could see it

that way if you want to as well

let's try this example 3.56

times 10 to the third power

so we need to move the decimal 3 units

to the right

so this is one two three so we need to

add another zero

so therefore this is going to be three

thousand five hundred and sixty

so ten to the third

means that well ten times ten times ten

that's a thousand with three zeros

and three point five six times a

go ahead and try these two examples

four point two seven times ten to the five

five

and also

three point nine six

so let's start with this one four point

two seven

let's move the decimal point five units

to the right

so we need to add three zeros

so this is going to be

four two seven

zero zero zero or four hundred twenty

seven thousand

ten to the fifth is basically a hundred thousand

thousand

so a hundred thousand times uh four

point two seven that's four hundred

twenty seven thousand

now let's try this one so we have three

point nine six

and we need to move the decimal point

seven units to the right so one two

and so we need to add

five zeros

so the answer is going to be three nine

six zero zero

zero zero zero

so that's 39 million six hundred thousand

now let's work on some examples with

negative exponents

so a negative exponent is going to be

associated with a small number so this time

time

we need to move to the left

so let's move three spaces to the left one

one two

two three

three

so we need to add two zeros so therefore

this is going to be

point zero zero

three seven

let's try this example four point one

so we need to move five spaces to the left

left one

one

so this is going to be point zero zero zero

zero

now let's work on a mixed review

go ahead and convert the following numbers

numbers

into scientific notation

so the first one is a small number so

it's going to be associated with a

negative exponent we need to move the

decimal point between the seven and the

three between the first two

non-zero numbers

so since we move it three units to the

right it's going to be 7.35

times ten to the negative three

now let's move on to the next example we

have a large number

and we need to put the decimal between

the first two non-zero numbers between

the three and six

so we're going to move it three four

five spaces to the left

so this is going to be 3.64

times 10 to the positive 5

since we have a large number

now the next example is a small number

and we only need to move it two spaces

to the left

so this is going to be 1.5

times 10 to the minus 2.

and for the last example

we have a large number and we're going

to move it three spaces to the left so

this is going to be

2.8 times 10 to the 3.

so keep that in mind anytime you have

positive exponents it always will be

associated with large numbers

and small numbers that are between 0 and 1

are associated with negative exponents

that will help you to determine which

direction you need to move the decimal point

so let's try some more examples

1.8 times 10 to the minus 3

four point one times ten to the two

one point two times ten to the negative five

five

and two point seven times ten to the four

four

so let's convert this to standard notation

notation

so let's start with the first example

should we move the decimal point to the

left or to the right

this is particularly useful if you need

to convert it from scientific notation

to standard form

since we have a negative exponent we

need a small number

so we got to move to the left

one two three

so we're going to fill these spaces with

zeros so therefore this is going to be .0018

now for the next example we have a

positive exponent

so that's associated with a large number

therefore we need to move the decimal

point to the right

two spaces

so we're going to add a zero here

therefore that's going to be 410.

now for the next example we need to move

it to the left one

so therefore that's going to be

point zero zero

and for the last one

we need to move it to the right

so hopefully this video gave you a good

introduction into scientific notation

and how to convert back and forth into

standard notation

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Scientific Notation - Fast Review!