https://file.aiquickdraw.com/mathbot/file/17288338662311uq4fzvw.jpg

The problem in the image requires you to calculate:

\[
\frac{4.46 \times 10^8}{8.53 \times 10^{-3}}
\]

and give the answer in standard form to 3 significant figures.

### Step 1: Division of the numbers
Let's separate the numerical parts from the powers of 10:
\[
\frac{4.46 \times 10^8}{8.53 \times 10^{-3}} = \frac{4.46}{8.53} \times 10^{8 - (-3)}
\]

First, calculate the powers of 10:
\[
10^{8 - (-3)} = 10^{8 + 3} = 10^{11}
\]

Next, divide the numbers:
\[
\frac{4.46}{8.53} \approx 0.5229
\]

So, we now have:
\[
0.5229 \times 10^{11}
\]

### Step 2: Adjust to standard form
Standard form requires the number to be between 1 and 10. So, we adjust:
\[
0.5229 \times 10^{11} = 5.229 \times 10^{10}
\]

### Step 3: Round to 3 significant figures
Rounding 5.229 to 3 significant figures gives:
\[
5.23 \times 10^{10}
\]

### Final Answer:
\[
5.23 \times 10^{10}
\]

Would you like more details on any of the steps?

Here are 5 related questions to expand your understanding:
1. How do you multiply numbers in standard form?
2. What rules apply when dividing powers of 10?
3. Why is it important to express answers in standard form?
4. How do you determine significant figures in a number?
5. Can you convert any number to standard form?

**Tip:** When working with large numbers, breaking them down into parts, like separating coefficients from powers of 10, simplifies calculations.

Use a calculator to work out \( \frac{4.46 \times 10^8}{8.53 \times 10^{-3}} \) and give your answer in standard form to 3 significant figures.

Learn how to solve the division of numbers in scientific notation: \( \frac{4.46 \times 10^8}{8.53 \times 10^{-3}} \). This step-by-step guide helps you understand powers of 10 and rounding to 3 significant figures, suitable for students in Grades 8-10.

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