Completed Density Calculations Worksheet I for Grade 9 Science, featuring solved problems on finding unknown quantities and word problems with handwritten answers.

You've uploaded a Density Calculations Worksheet I from Emond Montgomery Publications Limited, designed for Grade 9 Science (Atoms & Elements Unit). The worksheet includes basic density formula practice and word problems. All problems have been solved by hand — likely by a student or teacher — and you’re asking me to solve the problem and explain the solution.

Since the entire worksheet is already filled out with handwritten solutions, I’ll go through each section, verify the answers, and provide clear explanations so you understand *how* and *why* each solution works.

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## 🔢 SECTION 1: Find the Unknown Quantity

The core formula used throughout is:

> density (d) = mass (m) / volume (V)
> Rearranged as needed:
> - m = d × V
> - V = m / d

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a) Given: d = 3 g/mL, V = 100 mL → Find M

✔ Solution:
```
m = d × V
= (3 g/mL) × (100 mL)
= 300 g = 3 × 10² g
```

✔️ Explanation: Multiply density by volume to get mass. Units cancel appropriately (mL cancels), leaving grams. Scientific notation is used for large numbers.

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b) Given: V = 950 mL, M = 95 g → Find d

✔ Solution:
```
d = m / V
= 95 g / 950 mL
= 0.10 g/mL
```

✔️ Explanation: Divide mass by volume. Note that 95/950 = 0.1, but since we're dealing with measurements, it’s written as 0.10 g/mL to reflect two significant figures (from 95 g).

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c) Given: d = 0.5 g/cm³, M = 20 g → Find V

✔ Solution:
```
V = m / d
= 20 g / 0.5 g/cm³
= 40 cm³ = 4 × 10¹ cm³
```

✔️ Explanation: Volume = mass ÷ density. Units: grams cancel, leaving cm³. Also note: 1 cm³ = 1 mL, so this could also be expressed as 40 mL.

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## 🔄 SECTION 2: Convert First to g or mL

This section tests unit conversion before applying the density formula.

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a) d = 24 g/mL, V = 1.2 L → Find M

✔ Solution:
```
Convert 1.2 L to mL: 1.2 L × 1000 mL/L = 1200 mL
m = d × V = 24 g/mL × 1200 mL = 28,800 g = 2.88 × 10⁴ g
```

> ✍️ Handwritten answer says 2.9 × 10⁴ g — this is rounded to two significant figures, which is acceptable if following the rule of using the least number of sig figs in multiplication (24 has 2, 1.2 has 2 → so answer should have 2 sig figs).

✔️ Explanation: Always convert units to match before calculating. Liters to milliliters is essential here because density is given in g/mL.

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b) V = 100 mL, M = 1.5 kg → Find d

✔ Solution:
```
Convert 1.5 kg to grams: 1.5 kg × 1000 g/kg = 1500 g
d = m / V = 1500 g / 100 mL = 15.0 g/mL
```

✔️ Explanation: Kilograms must be converted to grams to match the mL unit in denominator. Answer is exact: 15.0 g/mL (three sig figs — 1.5 kg has two, but 100 mL may be considered exact if it's a measured cylinder volume; often treated as 3 sig figs).

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c) V = 0.52 L, M = 500 mg → Find d

✔ Solution:
```
Convert 0.52 L → 520 mL (×1000)
Convert 500 mg → 0.500 g (÷1000)
d = m / V = 0.500 g / 520 mL ≈ 0.0009615 g/mL = 9.62 × 10⁻⁴ g/mL
```

✔️ Explanation: Both mass and volume need conversion:
- mg → g (divide by 1000)
- L → mL (multiply by 1000)

Final answer is very small, so scientific notation is appropriate. The handwritten answer 9.62 × 10⁻⁴ g/mL is correct.

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## 📖 WORD PROBLEMS

These apply density calculations to real-world scenarios.

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1. Aluminum block: V = 15.0 mL, m = 40.5 g → Find d

✔ Solution:
```
d = m / V = 40.5 g / 15.0 mL = 2.70 g/mL
```

✔️ Explanation: Simple division. Both values have 3 significant figures, so answer is reported with 3 sig figs: 2.70 g/mL. This matches the known density of aluminum (~2.7 g/mL).

---

2. Mercury poured into cylinder: V = 22.5 mL, m = 306.0 g → Find d

✔ Solution:
```
d = m / V = 306.0 g / 22.5 mL = 13.6 g/mL
```

✔️ Explanation: Again, straightforward division. 306.0 has 4 sig figs, 22.5 has 3 → answer should have 3 sig figs → 13.6 g/mL. This matches the actual density of mercury (≈13.6 g/mL), confirming accuracy.

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## ✔ FINAL SUMMARY

All solutions on the worksheet are correct and well-explained with proper unit conversions and significant figures.

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## 🧠 KEY TAKEAWAYS FOR STUDENTS:

1. Always use the formula: d = m/V
2. Units must match! Convert kg→g, L→mL, mg→g, etc., before plugging into the formula.
3. Significant figures matter — round your final answer to match the least precise measurement.
4. 1 cm³ = 1 mL — useful for solids and liquids.
5. Density tells you how “compact” a material is — higher density = more mass per volume.

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## 💡 BONUS TIP:

Use the triangle method shown at the top right:

```
M
/ \
d V
```

Cover the variable you want to find:
- Cover M → d × V
- Cover d → M / V
- Cover V → M / d

It’s a great visual aid!

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Let me know if you’d like me to generate similar problems or create a quiz based on this worksheet! 😊