Question

Simplify the following notation (6.3 x 10^8)(8.4 x 10^-3)

Answer 1

Hello! What we need to do first in this kind of problem is multiply the numbers at be beginning of those notations. In this case, those numbers are 6.3 and 8.4. 6.3 * 8.4 is 52.92. We'll come back to this number in a bit. Now, let's worry about the exponents. When it comes to simplifiying scientific notations by multiplying, we need to add the exponents together. In this case, those are 8 and -3. 8 + (-3) is 5. Going back to 52.92, that number is greater than 10, so this will not work in scientifc notation. A number beign multiplied by a power of 10 is supposed to be greater than or equal to 1, but less than 10. We can make that number become less than 10 by moving the decimal to the left once to get 5.292. That works. But we're not done, now we must add 1 into the exponent, which is 5. 5 + 1 is 6. We can now write this in scientific notation:

5.292 * 10^6

There's our answer! That would be 5,292,000 in standard form, because 10^6 is 1,000,000. The notation simplified is 5.292 * 10^6.