KutaSoftware: Algebra 1- Operations With Scientific Notation Part 1 - Free Printable

Let's solve the problem step by step.

We are given the expression:

$$
(1.08 \times 10^{-3})(9.3 \times 10^{-3})
$$

This is a multiplication of two numbers in scientific notation.

---

Step 1: Multiply the coefficients

Multiply the decimal parts:

$$
1.08 \times 9.3
$$

Let’s compute that:

$$
1.08 \times 9.3 = ?
$$

Break it down:

$$
1.08 \times 9.3 = (1 + 0.08) \times 9.3 = 1 \times 9.3 + 0.08 \times 9.3 = 9.3 + 0.744 = 10.044
$$

So,

$$
1.08 \times 9.3 = 10.044
$$

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Step 2: Multiply the powers of 10

Now multiply the powers of 10:

$$
10^{-3} \times 10^{-3} = 10^{-3 + (-3)} = 10^{-6}
$$

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Step 3: Combine the results

Now combine the coefficient and the power of 10:

$$
10.044 \times 10^{-6}
$$

But this is not in proper scientific notation because the coefficient (10.044) is greater than 10. We need to adjust it.

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Step 4: Convert to proper scientific notation

We rewrite $10.044 \times 10^{-6}$ as:

$$
1.0044 \times 10^1 \times 10^{-6} = 1.0044 \times 10^{-5}
$$

Because:
- $10.044 = 1.0044 \times 10^1$
- So: $1.0044 \times 10^1 \times 10^{-6} = 1.0044 \times 10^{-5}$

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✔ Final Answer:

$$
\boxed{1.0044 \times 10^{-5}}
$$

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Additional Note:

The handwritten work in the image shows:
$$
(1.08 \times 9.3)(10^{-3} \times 10^{-3}) = 10.04 \times 10^{-6}
$$
That's correct, but not yet simplified. The final answer should be written in proper scientific notation: $1.0044 \times 10^{-5}$.

If rounding to significant figures is required (based on input), let's check:

- $1.08$ has 3 significant figures
- $9.3$ has 2 significant figures

So the result should have 2 significant figures.

Then:
$$
1.0044 \times 10^{-5} \approx \boxed{1.0 \times 10^{-5}}
$$

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✔ Final Answer (with appropriate significant figures):

$$
\boxed{1.0 \times 10^{-5}}
$$