Question

Find (4.8x10^6)(3.6x10^3)/(2x10^5), expressed in scientific notation.

8.64*10^4
8.64*10^6
8.64*10^8
17.28*10^4
17.28*10^8

Answer 1

To solve \((4.8 \times 10^6)(3.6 \times 10^3)/(2 \times 10^5)\), we will break it down step by step.

### Step 1: Multiply the numerators
\[
4.8 \times 10^6 \times 3.6 \times 10^3 = (4.8 \times 3.6) \times (10^6 \times 10^3)
\]
Calculating \(4.8 \times 3.6\):
\[
4.8 \times 3.6 = 17.28
\]
For the powers of 10:
\[
10^6 \times 10^3 = 10^{6 + 3} = 10^9
\]
So, the numerator becomes:
\[
17.28 \times 10^9
\]

### Step 2: Divide by the denominator
Now divide by \(2 \times 10^5\):
\[
\frac{17.28 \times 10^9}{2 \times 10^5} = \frac{17.28}{2} \times \frac{10^9}{10^5}
\]
Calculating \(\frac{17.28}{2}\):
\[
\frac{17.28}{2} = 8.64
\]
For the powers of 10:
\[
\frac{10^9}{10^5} = 10^{9 - 5} = 10^4
\]
So the result is:
\[
8.64 \times 10^4
\]

### Final Answer
Thus, the computed value in scientific notation is:
\[
\boxed{8.64 \times 10^4}
\]