Question

How do you convert numbers from real to scientific notation...?

Answer 1

the genral form Ax10^n
A<10

Answer 2

scientific notation is just a way to take large huge massively gigantic numbers and write them in a small compact way

Answer 3

simply by moving the decimal over so that it represents a number between 1 and 9 inclusive

Answer 4

so can you give an example?

Answer 5

Like 1,061.8

Answer 6

lol..

13,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Answer 7

ok, that works too ...lol

Answer 8

1.3 x 10^61

Answer 9

not to mention itty bitty numbers like
\[0.000 000 000 000 000 000 000 1\]

Answer 10

it works the other way for gigantically small numbers to

Answer 11

good morning!

Answer 12

howdy :)

Answer 13

did you really count that...lol

Answer 14

i like gigantically small. can i use that?

Answer 15

yes you can :)

Answer 16

i surely will. probably before the day is out
thanks

Answer 17

i counted 20 sets of 000, gives me 60 zeros, +1 more for the 3

Answer 18

so if it is 1061.8 you move it left 3 times

Answer 19

yes

Answer 20

from there, what is 10^n

Answer 21

see how easy this makes big numbers. by counting amstre wrote
\[1.3\times 10^{21}\]

Answer 22

10^(how many spots you moved the decimal)

Answer 23

wait.. so what is the number?

Answer 24

x*10^3

Answer 25

what will x be?

Answer 26

x means "times"

Answer 27

oh, sorry i meant

Answer 28

1061.8 = 1.0618 "times" 10^3

Answer 29

what will the decimal be

Answer 30

1061.8 x10^0

106.18 x10^1

10.618 x10^2

1.0618 x10^3

Answer 31

ohhh

Answer 32

you do know that 10^0 = 1 right?

Answer 33

but i remember hearing that you put how much numbers there are after / before the decimal to be the exponent

Answer 34

and yes

Answer 35

lets take 158

how can we fit this number between 1 and 9 ??

Answer 36

1 and 9?

Answer 37

1.58^2

Answer 38

158 x10^0 = 158: doesnt fit

158 x10^1 = 15.8: doesnt fit, still to big

158 x10^2 = 1.58: thatll fit between 1 and 9

Answer 39

oops, 1.58(times) 10^2

Answer 40

and i choose the upper of 9, but that is inherently a fault of mine lol

Answer 41

:)

Answer 42

we want to make it start with an integer from 1 to 9

Answer 43

oh yes

Answer 44

so can i tell you some from my worksheet and tell me if i did it right?

Answer 45

lets take a small number; and make it fit the bill

.000345 falls thru the netting, its way to small; how would we make it fit?

Answer 46

you can

Answer 47

err... 3.45 X 10^4?

Answer 48

youve got the idea right, but the wrong exponent :) youve just made it alot smaller that way

Answer 49

oh would it be negative?

Answer 50

yep

Answer 51

wait, so negative means you draw the decimal point to the right
and positive, left?

Answer 52

we need to divide by 10s to make it bigger now; and a negative exponent is notation for division

Answer 53

\[N*\frac{1}{10^3}=N *10^{-3}\]

Answer 54

it would be nice to remember a pattern, but its more helpful just to understand what the math is doing :)

Answer 55

so if it's a decimal already, the scientific notation would be negative

Answer 56

yes

Answer 57

like decimal from thebeginning

Answer 58

yep

Answer 59

hmm..

Answer 60

so it would be

Answer 61

Waaaait.. GRR

Answer 62

i just forgot.. if it was 0.01233

Answer 63

are you trying to put it like 1.233 X 10^2?

Answer 64

like make the first number be the first whole number

Answer 65

yes, but since its a decimal already, we divide by 10s

\[\frac{0.01233}{10^0}\]
\[\frac{00.1233}{10^1}\]
\[\frac{001.233}{10^2}\]
\[1.233\ x10^{-2}\]

Answer 66

uh...sorry im getting lost with the division. why do you need to divide?

Answer 67

in fact, that seems to be more intuitive than any other way i see :)... start out with the 10 underneath and that way the decimals moves in the same direction as the exponent

Answer 68

a negative exponent IS division

Answer 69

oh....

Answer 70

and its negative because it goes to the right

Answer 71

so how many zeroes, you divide by

Answer 72

watch this; im going to take 541.56 and change it ... go ahead and stick it over the 10^0

\[\frac{541.56}{10^0}\]

now as you move to the decimal to the left, you feel like your going in the negative direction correct?; so go negative on the exponent.

\[\frac{541.56}{10^0}\]
\[\frac{5.4156}{10^{-2}}\]
now when you bring up the 10, change the sign of the exponent, since thats what bringing up a denominator does ....

\[\frac{5.4156}{10^{-2}} =\ 5.4156\ x10^{2}\]

Answer 73

so it would be like

Answer 74

when you are dividing or multiplying

Answer 75

you try to make it go to the direction to get it smaller or bigger

Answer 76

yes

Answer 77

ok sorry just reading somehting over in my worksheet

Answer 78

lets work out a worksheet problem, go ahead and post one

Answer 79

112.94, i got 1.1294 X 10^2

Answer 80

its correct;

112.94 /10^0

11.294 /10^-1

1.1294 /10^-2

1.1294 x10^2

Answer 81

1679.7, i got 1.6797 X 10^3

Answer 82

wait

Answer 83

yes

Answer 84

oh nevermind i mistaken the decimal as comma ok

Answer 85

then 0.0000685 6.85 X 10^6

Answer 86

i try to think of that when its too small, youre trying to make it bigger, closer to 0

Answer 87

0.0000685 / 10^0

00.000685 / 10^1

0000.0685 / 10^3

000006.85 / 10^5

6.85 / 10^5

6.85 x10^-5

Answer 88

oh yes wsorry

Answer 89

why is it 5?

Answer 90

ohhhh

Answer 91

i went one over to the 0.

Answer 92

i went tried to go backwards