Practice worksheet for learning significant figures and scientific notation in chemistry.

Let's solve each part of the Practice Worksheet for Significant Figures step by step.

---

1. State the number of significant digits in each measurement.

We apply the rules for significant figures:

- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before the first non-zero digit) are not significant.
- Trailing zeros are significant only if there is a decimal point.

#### Answers:
1. 2804 m → 4 significant digits
*(All digits are non-zero)*

2. 2.84 km → 3 significant digits
*(All digits are non-zero)*

3. 5.0239 → 5 significant digits
*(All digits are significant, including zero between non-zeros)*

4. 0.003368 m → 4 significant digits
*(Leading zeros not significant; 3368 are significant)*

5. 4.6 × 10⁸ m → 2 significant digits
*(Only 4 and 6 are significant; exponent doesn't affect sig figs)*

6. 4.00 × 10⁻⁴ m → 3 significant digits
*(The two zeros after 4 are significant because they're trailing and after a decimal)*

7. 750 m → 2 significant digits
*(Trailing zero without decimal is ambiguous, but generally considered not significant unless specified)*

8. 75 m → 2 significant digits
*(Both digits are non-zero)*

9. 0.03 m → 1 significant digit
*(Only the 3 is significant; leading zeros don’t count)*

10. 79,000.0 m → 6 significant digits
*(Decimal point makes trailing zeros significant)*

11. 10 cm → 2 significant digits
*(Assuming it’s written as "10" with no decimal — usually interpreted as 2 sig figs if it's measured)*

> ⚠️ Note: If "10" had no decimal, it might be ambiguous. But in most contexts like this, it's treated as 2 significant figures.

---

2. Round the following numbers as indicated.

We round based on the number of significant figures or decimal places requested.

#### To two sig figs:
- 3,482,817 → 3,500,000
*(Rounded to 3.5 × 10⁶)*
- 375,6023 → 380,000
*(Wait: 375,6023 seems like a typo. Probably meant 375,602.3? Let's assume 375,602 → rounded to 380,000)*
- 113,811 → 110,000
*(Rounded to 1.1 × 10⁵)*
- 45.4673 → 45
*(Two sig figs: 45)*

#### To one sig fig:
- 41.87 → 40
*(Rounded to nearest ten)*
- 2.473 → 2
*(Rounded to nearest whole number)*
- 5.687524 → 6
*(Rounded up)*
- 125.3 → 100
*(Rounded to nearest hundred)*
- 8.235 → 8
*(Rounded to nearest unit)*

#### To two sig figs (again):
- 22,494 → 22,000
*(2.2 × 10⁴)*
- 79.2588 → 79
*(Already two sig figs? Wait: 79 has two sig figs, so keep as 79)*
- 0.03962 → 0.040
*(Two sig figs: 4.0 × 10⁻²)*
- 3,4125 → 3,400
*(3.4 × 10³)*
- 41.86632 → 42
*(42 has two sig figs)*

> ✔ So corrected:
- 22,494 → 22,000
- 79.2588 → 79
- 0.03962 → 0.040
- 3,4125 → 3,400
- 41.86632 → 42

---

3. Express the following numbers in their equivalent standard notational form. Then identify how many sig figs are in the number.

#### Standard Notation = Scientific Notation

Rules:
- Move decimal so that only one non-zero digit is to the left.
- Count significant digits.

| Number | Scientific Notation | Sig Figs |
|--------|---------------------|---------|
| 1) 133,476.3 | 1.334763 × 10⁵ | 7 |
| 2) 1,216,800 | 1.2168 × 10⁶ | 5 |
| 3) 42300 | 4.23 × 10⁴ | 3 |
| 4) 0.000000000000213 | 2.13 × 10⁻¹³ | 3 |
| 5) 0.004238 | 4.238 × 10⁻³ | 4 |
| 6) 0.0002305 | 2.305 × 10⁻⁴ | 4 |

> Explanation:
- For 42300, no decimal → trailing zeros not significant → only 4,2,3 are significant → 3 sig figs
- For 0.000000000000213, only the 213 are significant → 3 sig figs
- For 0.004238, leading zeros ignored → 4238 → 4 sig figs
- For 0.0002305, zeros before 2 not significant; 2305 → all four digits significant → 4 sig figs

---

✔ Final Answer Summary:

#### Part 1: Significant Digits
1. 4
2. 3
3. 5
4. 4
5. 2
6. 3
7. 2
8. 2
9. 1
10. 6
11. 2

#### Part 2: Rounding

To two sig figs:
- 3,482,817 → 3,500,000
- 375,602 → 380,000
- 113,811 → 110,000
- 45.4673 → 45

To one sig fig:
- 41.87 → 40
- 2.473 → 2
- 5.687524 → 6
- 125.3 → 100
- 8.235 → 8

To two sig figs (again):
- 22,494 → 22,000
- 79.2588 → 79
- 0.03962 → 0.040
- 3,4125 → 3,400
- 41.86632 → 42

#### Part 3: Scientific Notation & Sig Figs

| Number | Scientific Notation | Sig Figs |
|--------|---------------------|---------|
| 1) 133,476.3 | 1.334763 × 10⁵ | 7 |
| 2) 1,216,800 | 1.2168 × 10⁶ | 5 |
| 3) 42300 | 4.23 × 10⁴ | 3 |
| 4) 0.000000000000213 | 2.13 × 10⁻¹³ | 3 |
| 5) 0.004238 | 4.238 × 10⁻³ | 4 |
| 6) 0.0002305 | 2.305 × 10⁻⁴ | 4 |

---

✔ This completes the worksheet. Let me know if you'd like this formatted as a printable PDF or need explanations for any specific rule!