Final answer:
The product of 8300 and 7.7 × 10²⁷ is first calculated by converting 8300 to scientific notation (8.3 × 10³), then multiplying it by 7.7 × 10²⁷, and finally adjusting the result to proper scientific notation: 6.391 × 10³¹.
Step-by-step explanation:
To calculate the product of 8300 and 7.7 × 10²⁷, we must first express 8300 in scientific notation:
8300 = 8.3 × 10³.
Now, we can multiply this by 7.7 × 10²⁷:
(8.3 × 10³) × (7.7 × 10²⁷) = (8.3 × 7.7) × 10³× 10²⁷.
First, we multiply the coefficients (8.3 × 7.7) and then add the exponents (3 + 27), resulting in:
(63.91) × 10³⁰.
Finally, to express in proper scientific notation, we need to adjust the coefficient to have only one digit to the left of the decimal point:
6.391 × 10± (this is because we made the coefficient smaller by a factor of 10, so we increase the exponent by 1).
So the product in scientific notation is:
6.391 × 10³¹.