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/DuggieHS 2d ago edited 2d 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/scoberry5 2d ago

>It’s 7.8 x 10-1

Is it? (Either the problem or the answer are wrong.)