Multiplication and Division with Scientific Notation Worksheets - Free Printable

It looks like you're asking for help with a worksheet on scientific notation, specifically focusing on multiplication and division. However, I don't see the image you mentioned — perhaps it didn't upload properly.

But based on your description, I can help you solve typical problems from such a worksheet. Let me walk through common types of problems and show how to solve them step by step.

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🔢 Scientific Notation: Multiplication & Division

Scientific notation is written as:
$$
a \times 10^n
$$
where $1 \leq |a| < 10$ and $n$ is an integer.

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✔ Rules:

- Multiplication:
$(a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n}$

- Division:
$\frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m-n}$

After multiplying or dividing, adjust the result so that the coefficient is between 1 and 10.

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🧩 Example Problems (Common Types)

Let’s assume the worksheet has problems like these:

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#### Problem 1:
Simplify: $(3.2 \times 10^4) \times (2.5 \times 10^3)$

Step-by-step:

1. Multiply the coefficients:
$3.2 \times 2.5 = 8.0$

2. Add the exponents:
$10^4 \times 10^3 = 10^{4+3} = 10^7$

3. Combine:
$8.0 \times 10^7$

✔ Final answer: $8.0 \times 10^7$

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#### Problem 2:
Simplify: $(6.4 \times 10^6) \div (2.0 \times 10^2)$

Step-by-step:

1. Divide the coefficients:
$6.4 \div 2.0 = 3.2$

2. Subtract the exponents:
$10^6 \div 10^2 = 10^{6-2} = 10^4$

3. Combine:
$3.2 \times 10^4$

✔ Final answer: $3.2 \times 10^4$

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#### Problem 3:
Simplify: $(9.0 \times 10^{-3}) \times (4.5 \times 10^5)$

Step-by-step:

1. Multiply coefficients:
$9.0 \times 4.5 = 40.5$

2. Add exponents:
$10^{-3} \times 10^5 = 10^{2}$

3. Now we have: $40.5 \times 10^2$

But $40.5$ is not in proper scientific notation (must be $1 \leq a < 10$).

So adjust:
$40.5 = 4.05 \times 10^1$

Now:
$4.05 \times 10^1 \times 10^2 = 4.05 \times 10^{3}$

✔ Final answer: $4.05 \times 10^3$

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#### Problem 4:
Simplify: $(8.1 \times 10^7) \div (3.0 \times 10^4)$

1. Divide coefficients:
$8.1 \div 3.0 = 2.7$

2. Subtract exponents:
$10^7 \div 10^4 = 10^{3}$

3. Result: $2.7 \times 10^3$

✔ Final answer: $2.7 \times 10^3$

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📌 Tips:

- Always multiply/divide the decimal parts first.
- Then add/subtract the exponents.
- If the decimal part is not between 1 and 10, adjust by moving the decimal and changing the exponent accordingly.

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If you can describe or list the specific problems from your worksheet, I can solve them exactly for you!

Alternatively, if you’re able to upload the image again, I’ll be happy to analyze it directly.