To perform the multiplication of two numbers expressed in scientific notation, you need to follow these steps:
1. Multiply the coefficients (numeric part).
2. Add the exponents of the base 10.
Given the numbers:
[tex]\(9.25 \times 10^{-8}\)[/tex] and [tex]\(6.40 \times 10^3\)[/tex]
Let's proceed step-by-step:
### Step 1: Multiply the coefficients
The coefficients are 9.25 and 6.40.
Multiplying these together:
[tex]\[ 9.25 \times 6.40 = 59.2 \][/tex]
### Step 2: Add the exponents
The exponents are [tex]\(-8\)[/tex] and [tex]\(3\)[/tex].
Adding these together:
[tex]\[ -8 + 3 = -5 \][/tex]
### Conclusion
Combining the results from each step, the final product expressed in scientific notation is:
[tex]\[ 59.2 \times 10^{-5} \][/tex]
Therefore, the coefficient should be placed in the green box and the exponent in the yellow box:
- Coefficient: [tex]\(59.2\)[/tex]
- Exponent: [tex]\(-5\)[/tex]
