Question

when this expression (7.28x10^6)(5.13x10^4) is evaluated can someone help me out with finding the product written in scientific notation.

Answer 1

To multiply two numbers in scientific notation, multiply the number parts together, then add the exponents of 10. Then you may need to change the decimal point and exponent to make it a scientific notation number again.
Start with: what is 7.28 x 5.13?

Answer 2

37.3464

Answer 3

Great. Now the second part is the 10^6 x 10^4. When you multiply two powers with the same base you add the exponents. What is 10^6 x 10^4?

Answer 4

10^10 right?

Answer 5

Correct.
Then (7.28x10^6)(5.13x10^4) = 37.3 x 10^10
The result is correct, except it is not in scientific notation because in scientific notation, the number part has to be at least 1 and less than 10. We have 37.3 which is greater than 10.
We need to adjust the number and the exponent to make it scientific notation.

Answer 6

By changing the position of the decimal point one place to the left, the number in scientifice notation becomes 10 times smaller, so to compensate, you increase the exponent of the 10 by 1 to make the number 10 times larger. This way the number remains the same.