What is the correct expression of 34,000 x 96,000 using scientific notation?

To express \(34,000 \times 96,000\) in scientific notation, follow these steps:

### Step 1: Express each number in scientific notation
- \(34,000 = 3.4 \times 10^4\)
- \(96,000 = 9.6 \times 10^4\)

### Step 2: Multiply the coefficients and the powers of 10
Now, multiply the two numbers:
\[
(3.4 \times 10^4) \times (9.6 \times 10^4)
\]

This can be split into two parts:
1. Multiply the coefficients: \(3.4 \times 9.6\)
2. Multiply the powers of 10: \(10^4 \times 10^4\)

### Step 3: Perform the multiplication
- \(3.4 \times 9.6 = 32.64\)
- \(10^4 \times 10^4 = 10^{8}\)

So,
\[
34,000 \times 96,000 = 32.64 \times 10^8
\]

### Step 4: Adjust to correct scientific notation form
Scientific notation requires the coefficient to be between 1 and 10. So, we express \(32.64\) as \(3.264 \times 10^1\):

\[
32.64 \times 10^8 = 3.264 \times 10^1 \times 10^8 = 3.264 \times 10^9
\]

### Final Answer:
The correct expression of \(34,000 \times 96,000\) in scientific notation is:
\[
\boxed{3.264 \times 10^9}
\]

Would you like more details on any step? Here are five related questions:

1. How do you convert large numbers to scientific notation?
2. What is the process for multiplying two numbers in scientific notation?
3. How do you handle significant figures in scientific notation?
4. What is the advantage of using scientific notation for large numbers?
5. How do you divide two numbers in scientific notation?

**Tip:** When multiplying numbers in scientific notation, remember to first multiply the coefficients, then add the exponents of 10.

Learn how to express 34,000 × 96,000 in scientific notation with detailed steps. This problem involves converting large numbers to scientific notation, multiplying numbers in scientific notation, and adjusting coefficients to fit scientific notation rules. Suitable for students in Grades 6-8.

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