Question

The mass of a freight train is 9.98 ⋅ 10^6 kilograms. The mass of an aircraft carrier is 7.3 ⋅ 10^7 kilograms. Approximately how many more kilograms is the mass of an aircraft carrier than the mass of a freight train? Show your work and write your answer in scientific notation.

Answer 1

Welcome to OpenStudy! Have you tried anything so far? Any ideas on where to begin? :)

Answer 2

I'm Actually Not New xD My Old Account Got Hacked .-. But Thank You Hun cx Umm I was Thing to subtract the decimals and add the Exponents together

Answer 3

Oh that's fun... Well welcome back in that case. :)

Answer 4

Thank You But Is That Right? to subtract the decimals and add the Exponents together?

Answer 5

Um... I would want to be a bit careful... adding the exponents together would only make sense if we are multiplying. Let's set up the question.

Answer 6

We are trying to find this: (7.3 x 10^7) - (9.96 x 10^6)

Answer 7

Wait Its Subtraction so i subtract the decimals right?

Answer 8

That's right, but we can only add/subtract the decimals if the power of ten is the same for both.

Answer 9

Ok so i subract 7300000-996000?

Answer 10

I think you are just missing a zero on each of those, but yes, that's a good idea to convert before subtracting.

Answer 11

73,000,000 - 9,980,000

Answer 12

Ok so its 63040000 then when i convert it its 6.304 x 10 ^8 ?

Answer 13

You are off by a zero again... :) Let's check how you are counting your zeros...

Would you say that 1400 is 1.4 x 10^3 or 1.4 x 10^4 ?

Answer 14

Huh?

Answer 15

The answer should be 6.304 x 10^7 not 10^8. I want to see how you are deciding what to put for your power of ten.

Answer 16

So as a check, how would you write 1400 in scientific notation (just as a sample question)?

Answer 17

1.4 x 10 ^3?

Answer 18

Good! I guess you just miscounted the first time for the 6.304 answer. :)

Answer 19

Yeah xD I have Eye issues to its hard to look at the screen O-o

Answer 20

That probably makes doing scientific calculation miserable... sorry you have to suffer through this part of math. :(

Answer 21

But, yes it looks like you have the correct answer now. When in doubt convert and do normal math. :)

Answer 22

Its ok :D I just pushes me to work harder but i have a question

Answer 23

Sure, go ahead.

Answer 24

2^8 ⋅ 5^−5 ⋅ 19^0)^−2 ⋅ 5 to the power of negative 2 over 2 to the power of 3, whole to the power of 4 ⋅ 2^28

Answer 25

is one of the equations i completed it but i think its wrong :( Would you mind checking it for me?

Answer 26

Whoa... let me try retyping that first to make sure we are doing the same problem.

Answer 27

This is what i got when i simplified it :
= (256 ⋅ 0.00032 ⋅ 1) ⋅ (0.005) ⋅ 2^28
= (149.011611938) ⋅ (0.005) ⋅ 268435456
= (0.74505805969) ⋅ 268435456
= 19.99 with the Vinculum symbol over the 9

Answer 28

Here is the print shot. its number 2

Answer 29

Oh thank you. that helps. :)

Answer 30

Your welcome cx

Answer 31

Looks like you might have forget to keep the (0.005) with a power of 4. You have (0.005) should be (0.005)^4 on step one.

Answer 32

damnit >.< Omg Thank you

Answer 33

lol, your welcome... continuing check...

Answer 34

i gotta do the whole squation again Dx

Answer 35

lol... looks like there was another error anyways on the computation of 256 * 0.00032. Don't know if that's a comfort or an annoyance. :)

Answer 36

So I agree that step 1 should look like (256 * 0.00032 * 1) * (0.005)^4 * 2^28.

Answer 37

Step 2: (Recalculate first parentheses 256 * ...) (Recalculate 0.005...). 2^28 = 268435456 is correct.

Answer 38

So wait 149.011611938=(256 * 0.00032 * 1) ?

Answer 39

no, (256* 0.00032 * 1) does not equal 149.011...

Answer 40

Are you doing this with a calculator (I hope)? :)

Answer 41

Yeah xD i got 0.08192?

Answer 42

Yes, that's better. :)

Answer 43

Ok xD so part two should look like = (0.08192) * (0.005)^4 * 268435456?

Answer 44

Yep

Answer 45

the calculator says 6.25e-10 O.o

Answer 46

Yes, this is the calculators way of telling you that the answer is 6.25 x 10^-10, it uses "e" to stand for "x 10^". Weird but true.

Answer 47

Im confused now

Answer 48

No worries, all you have is (0.08192)*(6.25 x 10^-10)*268435456

Answer 49

6.25 x 10^-10 is 0.000000000625 (nine zeros after decimal point). I'm actually assuming that they wanted you to use scientific notation to solve most of these problems since that makes it easier. Your answers won't be wrong if you convert, but it's easier to make mistakes.

Answer 50

So it should look like this?
= (256 * 0.00032 * 1) * (0.005)^4 * 2^28.
= (0.08192) * (0.005)^4 * 268435456
= (0.08192) * (6.25 x 10^-10) * 268435456
= (0.08192) * (0.000000000625) * 268435456

Answer 51

Yes! You've got it.

Answer 52

Yay cx

Answer 53

Just be careful typing that into a calculator... We'll see if it can handle it.

Answer 54

i got 5.12e-11=(0.08192) * (0.000000000625)

Answer 55

So did I. :)

Answer 56

Yay i did it right xD Lol so ten nines are the decimal?

Answer 57

Yes, ten zeros (I knew what you meant) after the decimal.

Answer 58

xD lol my bad ok

Answer 59

0.0000000000512?

Answer 60

phew.... lots of zeros, yes looks good.

Answer 61

Ok xD and then 0.0000000000512 * 268435456?

Answer 62

^Yep, that monster... :)

Answer 63

xD lol
the answer i got was 0.01374389534?

Answer 64

Yep, and it just keeps going... that is the answer.

Answer 65

Now, just invent a robot that can do this automatically...

Answer 66

xD that is too much work xD

Answer 67

lol, yep

Answer 68

= (256 * 0.00032 * 1) * (0.005)^4 * 2^28.
= (0.08192) * (0.005)^4 * 268435456
= (0.08192) * (6.25 x 10^-10) * 268435456
= (0.08192) * (0.000000000625) * 268435456
= 0.0000000000512 * 268435456
= 0.01374389534
Is the full answer?

Answer 69

Hold on one second... I have to fix something on what we did...

Answer 70

= (256 * 0.00032 * 1)^-2 * (0.005)^4 * 2^28.
= (0.08192)^-2 * (0.005)^4 * 268435456
= (0.08192)^-2 * (6.25 x 10^-10) * 268435456
= 149.0116119 * (0.000000000625) * 268435456
= (9.31323 x 10^-8) * 268435456
=

Answer 71

We forgot the -2 exponent on the first parentheses, total oversight on my part, so I recalculated with Excel.

Answer 72

>.<
Lol i knew i was right before xD

Answer 73

Yes, indeed you were... :)

Answer 74

Im so lost now xD

Answer 75

OK... Let's refresh what happened...

Answer 76

idk where to pick up from O.o

=

Answer 77

= (9.31323 x 10^-8) * 268435456

Let's start here.

Answer 78

Turns out this is 25... wow.

Answer 79

= (256 * 0.00032 * 1)^-2 * (0.005)^4 * 2^28.
= (0.08192)^-2 * (0.005)^4 * 268435456
= (0.08192)^-2 * (6.25 x 10^-10) * 268435456
= 149.0116119 * (0.000000000625) * 268435456
= (9.31323 x 10^-8) * 268435456
= 25?

Answer 80

yes

Answer 81

Ok

Answer 82

Aw man!... now I see it... We have the right answer, but we should have just left the numbers alone and multiplied the exponents according to the rules.

Then,
(2^8 x 5^-5 x 19^0)^-2 = 2^-16 x 5^10
(5^-2 / 2^3)^4 = 5^-8 / 2^12 = 5^-8 x 2^-12
and 2^28 is just 2^28.

Then we just get
2^-16 x 5^10 x 5^-8 x 2^-12 x 2^28
= 2^-28 x 5^2 x 2^28
= 5^2
= 25

Answer 83

IM so confused -.-

Answer 84

@satellite73 Can u help? since you're watching?

Answer 85

nvr mind then, just for future reference, like I said we have the right answer one way or the other. :)

Answer 86

= (256 * 0.00032 * 1)^-2 * (0.005)^4 * 2^28.
= (0.08192)^-2 * (0.005)^4 * 268435456
= (0.08192)^-2 * (6.25 x 10^-10) * 268435456
= 149.0116119 * (0.000000000625) * 268435456
= (9.31323 x 10^-8) * 268435456
= 25? is right thou or no

Answer 87

Yes that is right

Answer 88

ok xD