Question

(8.91 times 10 Superscript 2 Baseline) (3.3 times 10 Superscript 12 Baseline)

Answer 1

Answer:

  2.9403×10^15

Step-by-step explanation:

Your calculator can work this out for you.

  $(8.91\times10^2)(3.3\times10^{12})=(0.891\times10^3)(3.3\times10^{12})\\\\=(0.891\times3.3)(10^{3+12})=\boxed{2.9403\times10^{15}}$

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The applicable rule of exponents is ...

  (10^a)(10^b) = 10^(a+b)

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Additional comments

You can keep a product the same if you divide one factor by 10 and multiply the other factor by 10:

  8.91×10² = (8.91/10)(10×10²) = 0.891×10³

I like to "pre-scale" the numbers in a problem like this so that the product comes out in scientific notation with no adjustment needed. That is, the product of the two mantissas is a number between 1 and 10.

Here, you can tell the product of 8.91 and 3.3 will be more than 24, so scaling will be necessary. It is convenient to scale the larger mantissa to be less than 1 so the product comes out less than 10. That is why we made it 0.891×10³.