Question 9
1
Solve the following problem.
$6.2 \times 10^{6} \times 5.5 \times 10^{6}=$
ALL answers should be entered in scientific notation using a capital $X$ for the sign and the ${ }^{\wedge}$ to show the exponent the correct format is $9.52 \times 10^{\wedge} 4$
MacBook Pro

Step 1 ：The problem is asking to multiply two numbers in scientific notation. The multiplication of numbers in scientific notation can be done by multiplying the coefficients (the numbers before the exponent part) and adding the exponents.

Step 2 ：Let's denote the coefficients as 'a' and 'b', and the exponents as 'exp_a' and 'exp_b'. For the given problem, a = 6.2, b = 5.5, exp_a = 6, and exp_b = 6.

Step 3 ：The multiplication of the coefficients (a*b) results in 34.1 and the addition of the exponents (exp_a + exp_b) results in 12. Therefore, the result of the multiplication of \(6.2 \times 10^{6}\) and \(5.5 \times 10^{6}\) is \(34.1 \times 10^{12}\).

Step 4 ：However, in scientific notation, the coefficient should be a number between 1 and 10. Therefore, we need to adjust the coefficient and the exponent to fit this rule.

Step 5 ：We adjust the coefficient by moving the decimal point one place to the left, which gives us 3.41. To compensate for this, we add 1 to the exponent, giving us 13. Therefore, the adjusted result is \(3.41 \times 10^{13}\).

Step 6 ：Final Answer: The result of the multiplication of \(6.2 \times 10^{6}\) and \(5.5 \times 10^{6}\) is \(\boxed{3.41 \times 10^{13}}\).