Scientific notation practice worksheet with a snowflake theme for math students.

Let's solve each of the problems on the snowflake-shaped worksheet step by step. The goal is to write the answer in scientific notation, and round to the nearest tenth.

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🔷 Center Problem:

$$
(5.1 \times 10^3) \times 520,000
$$

First, write 520,000 in scientific notation:
$$
520,000 = 5.2 \times 10^5
$$

Now multiply:
$$
(5.1 \times 10^3) \times (5.2 \times 10^5) = (5.1 \times 5.2) \times 10^{3+5}
$$

Calculate:
- $5.1 \times 5.2 = 26.52$
- $10^{8}$

So:
$$
26.52 \times 10^8 = 2.652 \times 10^9
$$

Round to the nearest tenth:
$$
\boxed{2.7 \times 10^9}
$$

---

🔷 Top Problem:

$$
(6.5 \times 10^2)(4.13 \times 10^4)
$$

Multiply:
- $6.5 \times 4.13 = 26.845$
- $10^{2+4} = 10^6$

So:
$$
26.845 \times 10^6 = 2.6845 \times 10^7
$$

Round to nearest tenth:
$$
\boxed{2.7 \times 10^7}
$$

---

🔷 Top Right Problem:

$$
(9.3 \times 10^7) \div 23,000
$$

Write 23,000 in scientific notation:
$$
23,000 = 2.3 \times 10^4
$$

Now divide:
$$
\frac{9.3 \times 10^7}{2.3 \times 10^4} = \left(\frac{9.3}{2.3}\right) \times 10^{7-4}
$$

Calculate:
- $9.3 \div 2.3 \approx 4.0435$
- $10^3$

So:
$$
4.0435 \times 10^3 \approx 4.0 \times 10^3 \quad \text{(rounded to nearest tenth)}
$$

$$
\boxed{4.0 \times 10^3}
$$

---

🔷 Bottom Right Problem:

$$
(6.01 \times 10^5)(5.01 \times 10^9)
$$

Multiply:
- $6.01 \times 5.01 = 30.1101$
- $10^{5+9} = 10^{14}$

So:
$$
30.1101 \times 10^{14} = 3.01101 \times 10^{15}
$$

Round to nearest tenth:
$$
\boxed{3.0 \times 10^{15}}
$$

---

🔷 Bottom Problem:

$$
(3.5 \times 10^2)(1.1 \times 10^4)
$$

Multiply:
- $3.5 \times 1.1 = 3.85$
- $10^{2+4} = 10^6$

So:
$$
3.85 \times 10^6
$$

Round to nearest tenth:
$$
\boxed{3.9 \times 10^6}
$$

---

🔷 Bottom Left Problem:

$$
(5.2 \times 10^3) \div (1.7 \times 10^2)
$$

Divide:
- $\frac{5.2}{1.7} \approx 3.0588$
- $10^{3-2} = 10^1$

So:
$$
3.0588 \times 10^1 \approx 3.1 \times 10^1 \quad \text{(rounded to nearest tenth)}
$$

$$
\boxed{3.1 \times 10^1}
$$

---

🔷 Top Left Problem:

$$
(6.2 \times 10^3)(5.6 \times 10^5)
$$

Multiply:
- $6.2 \times 5.6 = 34.72$
- $10^{3+5} = 10^8$

So:
$$
34.72 \times 10^8 = 3.472 \times 10^9
$$

Round to nearest tenth:
$$
\boxed{3.5 \times 10^9}
$$

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✔ Final Answers (in order around the snowflake):

1. Top: $(6.5 \times 10^2)(4.13 \times 10^4)$ → $\boxed{2.7 \times 10^7}$
2. Top Right: $(9.3 \times 10^7) \div 23,000$ → $\boxed{4.0 \times 10^3}$
3. Bottom Right: $(6.01 \times 10^5)(5.01 \times 10^9)$ → $\boxed{3.0 \times 10^{15}}$
4. Bottom: $(3.5 \times 10^2)(1.1 \times 10^4)$ → $\boxed{3.9 \times 10^6}$
5. Bottom Left: $(5.2 \times 10^3) \div (1.7 \times 10^2)$ → $\boxed{3.1 \times 10^1}$
6. Top Left: $(6.2 \times 10^3)(5.6 \times 10^5)$ → $\boxed{3.5 \times 10^9}$
7. Center: $(5.1 \times 10^3) \times 520,000$ → $\boxed{2.7 \times 10^9}$

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📝 Summary of Steps:

- Convert all numbers to scientific notation.
- Use exponent rules:
- Multiply: add exponents
- Divide: subtract exponents
- Multiply coefficients.
- Round final result to nearest tenth (one decimal place).
- Express in proper scientific notation: $a \times 10^n$, where $1 \leq a < 10$

✔ All answers are now rounded and in scientific notation as required!