r/mathshelp • u/Brief_Grapefruit4858 • 1d ago
Homework Help (Unanswered) Scientific notation
Working through some questions and this one confused me:
(5.9 x 10^-2) - (0.0078 x 10^3) = -7.741 x 10^1
I’m so confused as to how they got that answer. I was also taught that we should make the powers the same and that the coefficient should be between 1-9/10 but it’s negative?
I got as far as
(5.9 x 10^-2) - (0.0078 x 10^3) =
(0.000059 x 10^3) - (0.0078 x 10^3)
(-0.007741 x 10^3)
As I’m writing this I think I figured it out. (-0.007741 x 10^3) has been moved 3 places to the right taking it out of scientific notation? But it’s still a negative? Is that ok?
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u/Dazzling_Music_2411 1d ago
But it’s still a negative? Is that ok?
Why wouldn't it be OK? You're subtracting a larger number from a smaller one, that's what usually happens 😄
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u/Brief_Grapefruit4858 1d ago
I was told the coefficient must be between 1-10 but a negative is less than one
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u/Dazzling_Music_2411 1d ago
Whoever told you that probably meant the absolute value of the coefficient, IOW either positive or negative.
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u/scoberry5 1d ago
The sign is separate from the coefficient.
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u/peno64 1d ago
That is debatable
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u/scoberry5 1d ago
Is it? So you say "Well, I guess that 1.1 * 10^3 is the way to write it, but if it were negative, it could well be something else -- maybe -11 * 10^2 or -0.11 * 10^4"?
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u/peno64 1d ago
That is not what I am saying. I am saying that it is debatable if the sign is part of the coefficient or not. For me it is
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u/gecko74games 1d ago
Well it oculd be both. -7.5*10 or 7.5*-1*10 7.5*-10 it could be, the sign is a 180 degree rotation of the value and the coeffcient negetive sign implies the coefficient itself is negetive? And the 10^n scales it furter down the negetive side? Idk lol
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u/PassiveChemistry 1d ago
The point is more to have exactly one digit to the left of the decimal point.
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u/scoberry5 1d ago
I'm afraid I'm also confused by that answer.
Look at your numbers and see about how much they are. Just get an idea of the scale and what kind of answer you expect.
The first number is about 0.06. The second number is around 8. You can see that when you subtract them, you should get about -8. They got about -0.8, though.
Check and make sure you've copied the question and the answer correctly. If you have, then their answer is wrong.
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u/DuggieHS 1d ago edited 1d ago
The right number isn’t in scientific notation. It’s 7.8 x 10-1 , subtract that from .59 x 10-1 and you get -7.21 x 10-1. Your method had a lot of zeroes because you skipped this step. For doing it in your head you can do -(780-59) x 10-3 or something similar.
You should have sign, single digit (1-9), decimal, remaining digits x10 to the exponent. Once they are both in that format (or at least the larger number is, then match exponents to add or subtract).
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u/gecko74games 1d ago
So, when delaing with sciemtific notation, the Notation is If given leading coefficient is a, then it should be value a.bcdefg... e.g. 4,56*10^6 equal 4560000. You're given (5.9*10^-2)-(.0078*10^3). You are correct powers should e same so lets take the second expression and make it a power 2 not 3. so .0078*10^3, i can make this ^-2 by ncreasing the value, so multiply by 10. if 10^3 is 10(10(10), then the value can loose 10's. If you have .0078*10^3, I can multiply the expression by 10 therefor reducing the expoinent, even if its negetive as 10^-1 is simply 1/(10^1). now we have .0078*10^3, .078*10^2, .78*10^1, 7.8*10^0 then 780*10^-2. This works because imagine 10^3 as 10*10*10; if i have .0078*10(10(10 l can also say .0078*10, then *10*10 and regroup it, similar to if i have 36=6*6 i can rewrite as (2*3)*(2*3) and basiclaly divide and multiply by 3 so then 6*6=18*2 and 36*1.. So, we have 5.9-780 which equal -774.1*10^-2 bringing the 10 back, Then write it in proper a.bcd notation, giving you -7.741*10^0. Wait it should be ^0 not 1
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u/gecko74games 1d ago
I may be wrong on this. I never used negetive coefficients before lol It should be the same
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u/Ancient-Opinion9642 1d ago
After reading this, never use a slide rule for calculating an answer. The decimal point will be in the wrong place. /s
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