Question

help:/

Determine if the number is written in scientific notation. If not explain.
1. 4.8x100^7

No; it is not written as a number times a power of 10
yes; the number is written in scienfic notation
no; the first factor is not a number between 1 and 10

2. 5.1x10^-8
yes; the number is written in scienfic notation
no; the first factor is not a number between 1 and 10
no; it is not written as a number times a power of 10

Answer 1

scientific notation follows the basic format

b x 10^n

where b is some number between 1 and 10 (NOT including 10 though)

and n is some integer

Answer 2

some numbers in scientific notation are:

2.3 x 10^7
8.1 x 10^(-5)
1.078 x 10^(12)

Answer 3

so what can you tell me about 4.8 x 100^7

Answer 4

i think 1 is b
and 2 is c

Answer 5

why 1 b

Answer 6

why do you think 4.8 x 100^7 is in scientific notation?

Answer 7

the base is 4.8

that's between 1 and 10 and it's not equal to 10

so that part works

Answer 8

but....

the 100 *should* be 10 if you look back to the basic format I wrote out

Answer 9

so its a

Answer 10

you got it

Answer 11

and 2 is what c?

Answer 12

the reason why 10 is chosen over 100 is because you can move the decimal one spot at a time (when you change the exponent by 1)

but with 100, you would have to move the decimal point twice per every change in exponent by 1

Answer 13

so that's why 100 doesn't really work out

Answer 14

5.1 is that between 1 and 10 (and not equal to 10)?

Answer 15

wait is it a?

Answer 16

very good

Answer 17

compare the basic form

b x 10^n

with

5.1x10^-8

and you'll see that b = 5.1 and n = -8

Answer 18

b = 5.1 is between 1 and 10 and not equal to 10

you have a power of 10

and the exponent is some integer

Answer 19

so it all works out

Answer 20

can u help me with more quuestions?

Answer 21

sure, just a few more though

Answer 22

What is the order of 1.5x10^3, 1.4x10^-1, 2x10^3, and 1.4x10^-2 from, least to greatest?

1.4x10^2, 1.4x10^-1, 1.5x10^3, 2x10^3
1.4x10^-1,1.4x10^2, 2x10^3, 1.5x10^3
2x10^3, 1.5x10^3, 1.4x10^-1, 1.4x10^-2
2x10^-3, 1.4x10^2, 1.5x10^3,1.4x10^-1


i thinki think it is A ?

Answer 23

2. Simplify this expression(-4)^-6(-4)^7

4^13
-4
13
1

is it A?

Answer 24

one at a time please

Answer 25

it might help to expand out each number

1.4x10^2 = 140 (move the decimal point 2 places to the right)

1.4x10^-1 = 0.14 (move the decimal point 1 place to the left)

2x10^3 = 2000 (move the decimal point 3 places to the right)

1.4x10^-2 = 0.014 (move the decimal point 2 places to the left)

Answer 26

so...

the list of numbers:

1.5x10^3, 1.4x10^-1, 2x10^3, and 1.4x10^-2

is really the same as this list of numbers (in the same order)

140, 0.14, 2000, 0.014

Answer 27

so it's your job to sort 1.5x10^3, 1.4x10^-1, 2x10^3, and 1.4x10^-2

but it might be easier to sort 140, 0.14, 2000, 0.014

Answer 28

from least to greatest

Answer 29

oh i missed one...sorry about that

1.5 x 10^3 = 1500

Answer 30

let me redo, one sec

Answer 31

1.5x10^3, 1.4x10^-1, 2x10^3, and 1.4x10^-2


1.5x10^3 = 1500

1.4x10^-1 = 0.14

2x10^3 = 2000

1.4x10^-2 = 0.014

Answer 32

I misread the initial list of numbers, but it's fixed now

Answer 33

so its 0.14, 0.014,140,1500,2000

Answer 34

sorry, 140 isn't part of the list

I misread and thought it was

Answer 35

so kick that out

Answer 36

0.014 is smaller than 0.14

so flip the two

Answer 37

so here is the correct order

0.014, 0.14, 1500, 2000

now convert back to scientific notation

Answer 38

to convert back, you just undo what we did above (so if we went 3 places to the right, we just go 3 places back to the left)

0.014 = 1.4 x 10^-2

0.14 = 1.4 x 10^-1

1500 = 1.5 x 10^3

2000 = 2 x 10^3

Answer 39

0.14, 0.014,1500,200

Answer 40

2000

Answer 41

yes

Answer 42

btw this problem has a few typos in it (I think, not 100% sure though)

for instance, in the original list, you refer to 1.4 x 10^-2 (the exponent is negative)

but in the first answer choice, you have 1.4 x 10^2 (but now the exponent is positive)

Answer 43

so it si a

Answer 44

i think so, if choice A is really

1.4x10^-2, 1.4x10^-1, 1.5x10^3, 2x10^3

then yes it is

Answer 45

. Simplify this expression(-4)^-6(-4)^7

4^13
-4
13
1

is it A?

Answer 46

The bases are the same

so you can add the exponents

Answer 47

-6+7 = ???

Answer 48

1

Answer 49

so the new exponent is now 1

Answer 50

therefore, we get (-4)^1 = ???

Answer 51

4

Answer 52

any number to the first power is that same number

Answer 53

x^1 = x

Answer 54

so its i -4

Answer 55

yep -4