Multiplying and Dividing in Scientific Notation - ppt download - Free Printable

Let's solve each problem step by step using the rules of multiplying numbers in scientific notation.

🔧 Rule for Multiplying in Scientific Notation:

When multiplying two numbers in scientific notation:

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

Then, if needed, adjust the result to proper scientific notation (i.e., ensure the coefficient is between 1 and 10).

---

Problem 1:

$$
(2.4 \times 10^{-3})(4.5 \times 10^{-3}) =
$$

- Multiply coefficients: $2.4 \times 4.5 = 10.8$
- Add exponents: $-3 + (-3) = -6$
- So: $10.8 \times 10^{-6}$

But $10.8$ is not in proper scientific notation (must be < 10), so we adjust:

$$
10.8 \times 10^{-6} = 1.08 \times 10^1 \times 10^{-6} = 1.08 \times 10^{-5}
$$

✔ Answer: $ \boxed{1.08 \times 10^{-5}} $

---

Problem 2:

$$
(5.67 \times 10^3)(3.9 \times 10^{-6}) =
$$

- Multiply coefficients: $5.67 \times 3.9 = 22.013$
- Add exponents: $3 + (-6) = -3$
- So: $22.013 \times 10^{-3}$

Adjust to proper scientific notation:

$$
22.013 \times 10^{-3} = 2.2013 \times 10^1 \times 10^{-3} = 2.2013 \times 10^{-2}
$$

✔ Answer: $ \boxed{2.2013 \times 10^{-2}} $

---

Problem 3:

$$
(4.78 \times 10^7)(9.3 \times 10^{-2}) =
$$

- Multiply coefficients: $4.78 \times 9.3 = 44.454$
- Add exponents: $7 + (-2) = 5$
- So: $44.454 \times 10^5$

Adjust:

$$
44.454 \times 10^5 = 4.4454 \times 10^1 \times 10^5 = 4.4454 \times 10^6
$$

✔ Answer: $ \boxed{4.4454 \times 10^6} $

---

Problem 4:

$$
(8.9 \times 10^{-2})(6.5 \times 10^4) =
$$

- Multiply coefficients: $8.9 \times 6.5 = 57.85$
- Add exponents: $-2 + 4 = 2$
- So: $57.85 \times 10^2$

Adjust:

$$
57.85 \times 10^2 = 5.785 \times 10^1 \times 10^2 = 5.785 \times 10^3
$$

✔ Answer: $ \boxed{5.785 \times 10^3} $

---

Problem 5:

$$
(3.4 \times 10^8)(5 \times 10^3) =
$$

- Multiply coefficients: $3.4 \times 5 = 17$
- Add exponents: $8 + 3 = 11$
- So: $17 \times 10^{11}$

Adjust:

$$
17 \times 10^{11} = 1.7 \times 10^1 \times 10^{11} = 1.7 \times 10^{12}
$$

✔ Answer: $ \boxed{1.7 \times 10^{12}} $

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✔ Final Answers:

1. $1.08 \times 10^{-5}$
2. $2.2013 \times 10^{-2}$
3. $4.4454 \times 10^6$
4. $5.785 \times 10^3$
5. $1.7 \times 10^{12}$

Let me know if you'd like these rounded to significant figures!