HW: Scientific Notation Multiplication and Division 12-04-2020 ... - Free Printable

Let's solve each problem on the Scientific Notation Multiplication and Division Worksheet step by step.

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🔷 Rules to Remember:

- Multiplication:
Multiply the decimal parts and add the exponents.
$$(a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n}$$

- Division:
Divide the decimal parts and subtract the exponents.
$$(a \times 10^m) \div (b \times 10^n) = (a \div b) \times 10^{m-n}$$

- Always express the final answer in proper scientific notation: one non-zero digit before the decimal point.

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Now, let's solve each problem:

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1. $(9.32 \times 10^3)(3.32 \times 10^2)$

- Multiply decimals: $9.32 \times 3.32 = 31.0024$
- Add exponents: $10^{3+2} = 10^5$
- So: $31.0024 \times 10^5$
- Convert to proper scientific notation: $3.10024 \times 10^6$

✔ Answer: $3.10024 \times 10^6$

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2. $(7.22 \times 10^1)(4.45 \times 10^3)$

- $7.22 \times 4.45 = 32.039$
- $10^{1+3} = 10^4$
- $32.039 \times 10^4 = 3.2039 \times 10^5$

✔ Answer: $3.2039 \times 10^5$

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3. $(6.82 \times 10^5)(3.77 \times 10^2)$

- $6.82 \times 3.77 = 25.6314$
- $10^{5+2} = 10^7$
- $25.6314 \times 10^7 = 2.56314 \times 10^8$

✔ Answer: $2.56314 \times 10^8$

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4. $(2.41 \times 10^4)(4.12 \times 10^2)$

- $2.41 \times 4.12 = 9.9192$
- $10^{4+2} = 10^6$
- $9.9192 \times 10^6$ → already in proper form

✔ Answer: $9.9192 \times 10^6$

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5. $(1.09 \times 10^2)(2.79 \times 10^1)$

- $1.09 \times 2.79 = 3.0311$
- $10^{2+1} = 10^3$
- $3.0311 \times 10^3$

✔ Answer: $3.0311 \times 10^3$

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6. $(5.26 \times 10^5) \div (11.1 \times 10^3)$

- Divide decimals: $5.26 \div 11.1 \approx 0.47387$
- Subtract exponents: $10^{5-3} = 10^2$
- $0.47387 \times 10^2 = 4.7387 \times 10^1$

✔ Answer: $4.7387 \times 10^1$

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7. $(5.75 \times 10^4) \div (4.7 \times 10^2)$

- $5.75 \div 4.7 \approx 1.2234$
- $10^{4-2} = 10^2$
- $1.2234 \times 10^2$

✔ Answer: $1.2234 \times 10^2$

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8. $(3.38 \times 10^6) \div (7.8 \times 10^4)$

- $3.38 \div 7.8 \approx 0.4333$
- $10^{6-4} = 10^2$
- $0.4333 \times 10^2 = 4.333 \times 10^1$

✔ Answer: $4.333 \times 10^1$

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9. $(17.04 \times 10^5) \div (19.4 \times 10^2)$

- First, write in proper scientific notation:
$17.04 \times 10^5 = 1.704 \times 10^6$
$19.4 \times 10^2 = 1.94 \times 10^3$

- Now divide:
$1.704 \div 1.94 \approx 0.87835$
- $10^{6-3} = 10^3$
- $0.87835 \times 10^3 = 8.7835 \times 10^2$

✔ Answer: $8.7835 \times 10^2$

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10. $(9.75 \times 10^6) \div (1.9 \times 10^2)$

- $9.75 \div 1.9 \approx 5.13158$
- $10^{6-2} = 10^4$
- $5.13158 \times 10^4$

✔ Answer: $5.13158 \times 10^4$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $3.10024 \times 10^6$ |
| 2 | $3.2039 \times 10^5$ |
| 3 | $2.56314 \times 10^8$ |
| 4 | $9.9192 \times 10^6$ |
| 5 | $3.0311 \times 10^3$ |
| 6 | $4.7387 \times 10^1$ |
| 7 | $1.2234 \times 10^2$ |
| 8 | $4.333 \times 10^1$ |
| 9 | $8.7835 \times 10^2$ |
| 10 | $5.13158 \times 10^4$ |

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Let me know if you'd like these rounded to a specific number of significant figures!