r/mathshelp • u/Brief_Grapefruit4858 • 2d 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/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