Final answer:
To calculate the product of 8.69 x 10^-6 and 5.5 x 10^-7, we multiply the coefficients and add the exponents, resulting in 4.7795 x 10^-12 in proper scientific notation.
Step-by-step explanation:
The problem asks to work out an equation involving numbers in scientific notation, which is a way to express very large or very small numbers. Here, the equation provided seems to be a mistake because it should be an expression, not an equation as equal signs signify a comparision between two values. Instead, let's assume you meant to calculate the product 8.69 x 10^-6 times 5.5 x 10^-7.
To calculate the product of two numbers in scientific notation, you multiply the coefficients (the numbers before the exponent) and add the exponents. Here's how you would do it:
- Multiply the coefficients: 8.69 * 5.5 = 47.795.
- Add the exponents: (-6) + (-7) = -13.
- Combine these to write the final product in scientific notation, which is 4.7795 x 10^-13. However, to keep it in proper scientific notation, we must have one non-zero digit to the left of the decimal point. So, move the decimal point one place to the right to get 4.7795 which becomes 4.7795, and adjust the exponent by one to compensate, so the exponent becomes -13+1 which is -12.
- The result in correct scientific notation format is: 4.7795 x 10^-12.
This process allows us to handle very large or very small numbers efficiently.