Worksheet for practicing significant figures and scientific notation calculations.

Absolutely! Let’s solve both problems step by step, explaining the rules for significant figures and how to apply them in calculations.

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## ✔ Problem 1: Determine the number of significant figures

🔑 Rules Recap:

- Non-zero digits are always significant.
- Leading zeros (before first non-zero digit) are NOT significant.
- Captive zeros (between non-zero digits) ARE significant.
- Trailing zeros in a number with a decimal point ARE significant.
- Trailing zeros in a whole number without a decimal are ambiguous — but if written with a decimal (e.g., 501.0), they are significant.
- In scientific notation, all digits in the coefficient are significant.

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a) 0.02

→ Leading zeros don’t count. Only “2” is significant.
✔ Answer: 1

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b) 0.020

→ Leading zeros don’t count. “2” and trailing zero after decimal do count.
✔ Answer: 2

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c) 501

→ All non-zero digits + captive zero → 3 significant figures.
✔ Answer: 3

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d) 6051.00

→ All digits are significant: 6,0,5,1, and two trailing zeros after decimal.
✔ Answer: 6

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e) 501.0

→ Same as above: captive zero + trailing zero after decimal = all significant.
✔ Answer: 4

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f) 2.000 × 10²

→ Coefficient is “2.000” → 4 significant figures.
✔ Answer: 4

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g) 0.982 × 10⁻³

→ This is same as 9.82 × 10⁻⁴ → coefficient “0.982” has 3 sig figs.
✔ Answer: 3

*(Note: Leading zero before decimal doesn’t count — only 9,8,2 are significant.)*

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h) 0.0114 × 10⁴

→ First, rewrite in proper scientific notation:
0.0114 × 10⁴ = 1.14 × 10²
→ Coefficient “1.14” has 3 significant figures.
✔ Answer: 3

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## ✔ Problem 2: Calculate using correct number of significant digits

🔑 Rules for Calculations:

- Multiplication/Division: Result has same number of sig figs as the factor with the least sig figs.
- Addition/Subtraction: Result is rounded to the least precise decimal place (i.e., the rightmost column where all numbers have digits).

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a) 1.35 × 2.467

→ 1.35 has 3 sig figs, 2.467 has 4 → answer must have 3 sig figs.
Calculation: 1.35 × 2.467 = 3.33045 → round to 3 sig figs → 3.33

✔ Answer: 3.33

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b) 1.035 + 4.2

→ 1.035 has precision to thousandths, 4.2 to tenths → answer must be to tenths.
Calculation: 1.035 + 4.2 = 5.235 → round to tenths → 5.2

✔ Answer: 5.2

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c) 12.01 + 35.2 + 6.9

→ 12.01 (hundredths), 35.2 (tenths), 6.9 (tenths) → least precise is tenths.
Sum: 12.01 + 35.2 + 6.9 = 54.11 → round to tenths → 54.1

✔ Answer: 54.1

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d) 55.46 − 28.9

→ 55.46 (hundredths), 28.9 (tenths) → answer to tenths.
Difference: 55.46 − 28.9 = 26.56 → round to tenths → 26.6

✔ Answer: 26.6

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e) 0.21 × 3.2 × 100.1

→ Sig figs: 0.21 (2), 3.2 (2), 100.1 (4) → least is 2 sig figs.
Product: 0.21 × 3.2 = 0.672; × 100.1 = 67.2672 → round to 2 sig figs → 67

✔ Answer: 67

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f) 505.0 − 450.25

→ 505.0 (tenths), 450.25 (hundredths) → least precise is tenths.
Difference: 505.0 − 450.25 = 54.75 → round to tenths → 54.8

✔ Answer: 54.8

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g) 1.5 × 10⁶ / 3.76 × 10²

→ 1.5 has 2 sig figs, 3.76 has 3 → answer has 2 sig figs.
Calculation: (1.5 / 3.76) × 10⁶⁻² = 0.398936... × 10⁴ = 3.98936 × 10³
→ Round to 2 sig figs → 4.0 × 10³

✔ Answer: 4.0 × 10³

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h) 1.28 × 10³ / 1.4267 × 10²

→ 1.28 has 3 sig figs, 1.4267 has 5 → answer has 3 sig figs.
Calculation: (1.28 / 1.4267) × 10¹ ≈ 0.8971 × 10¹ = 8.971
→ Round to 3 sig figs → 8.97

✔ Answer: 8.97

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## 📝 Final Answers:

Problem 1:

a) 1
b) 2
c) 3
d) 6
e) 4
f) 4
g) 3
h) 3

Problem 2:

a) 3.33
b) 5.2
c) 54.1
d) 26.6
e) 67
f) 54.8
g) 4.0 × 10³
h) 8.97

Let me know if you’d like these formatted into a printable worksheet or explained further!