Sure, let's go through the calculation step-by-step.
### Step 1: Write the numbers in scientific notation
We have two numbers given in scientific notation:
- [tex]\(4.0 \times 10^5\)[/tex]
- [tex]\(3.0 \times 10^3\)[/tex]
### Step 2: Multiply the coefficients
First, we need to multiply the coefficients (the numbers before the powers of 10):
[tex]\[ 4.0 \times 3.0 = 12.0 \][/tex]
### Step 3: Add the exponents
Next, we add the exponents of the powers of 10:
[tex]\[ 10^5 \times 10^3 \][/tex]
When multiplying exponents with the same base, we add the exponents:
[tex]\[ 5 + 3 = 8 \][/tex]
So,
[tex]\[ 10^5 \times 10^3 = 10^8 \][/tex]
### Step 4: Combine the results
Now we combine the result of the multiplication of the coefficients with the result of the exponent addition:
[tex]\[ 12.0 \times 10^8 \][/tex]
### Step 5: Express in correct scientific notation
To express this in correct scientific notation, the coefficient should be a number between 1 and 10. Therefore, we adjust it as follows:
[tex]\[ 12.0 \times 10^8 = 1.2 \times 10 \times 10^8 = 1.2 \times 10^9 \][/tex]
So, the final answer in correct scientific notation is:
[tex]\[ 1.2 \times 10^9 \][/tex]
Therefore, multiplying [tex]\(4.0 \times 10^5\)[/tex] and [tex]\(3.0 \times 10^3\)[/tex] gives [tex]\( 1.2 \times 10^9 \)[/tex] in scientific notation.
