Significant Figures & Scientific Notation worksheet - Free Printable

Activity 1: Significant Figures and Scientific Notation

#### A. Find the number of significant digits in the following measurements.

1. 10100 mm
- Significant digits: 4 (The zeros at the end are not significant unless there is a decimal point.)
- Answer: 4

2. 0.087400 cL
- Significant digits: 5 (Leading zeros are not significant, but trailing zeros after the decimal point are significant.)
- Answer: 5

3. 170.5 km
- Significant digits: 4 (All non-zero digits and the zero between non-zero digits are significant.)
- Answer: 4

4. 5000 cm³
- Significant digits: 1 (Without a decimal point, only the first non-zero digit is significant.)
- Answer: 1

5. 36 kg
- Significant digits: 2 (All non-zero digits are significant.)
- Answer: 2

6. 3.500 × 10⁻² s
- Significant digits: 4 (All digits in scientific notation are significant.)
- Answer: 4

7. 6.19 × 10⁻¹ mi
- Significant digits: 3 (All digits in scientific notation are significant.)
- Answer: 3

8. 1.00 × 10³ mg
- Significant digits: 3 (All digits in scientific notation are significant.)
- Answer: 3

9. 2 × 10² °C
- Significant digits: 1 (Only the digit "2" is significant.)
- Answer: 1

10. 5.920 × 10⁻¹ A
- Significant digits: 4 (All digits in scientific notation are significant.)
- Answer: 4

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#### B. Write the following measurements in the scientific notation format.

1. 10100 mm
- Scientific notation: \( 1.0100 \times 10^4 \)
- Answer: \( 1.0100 \times 10^4 \)

2. 0.087400 cL
- Scientific notation: \( 8.7400 \times 10^{-2} \)
- Answer: \( 8.7400 \times 10^{-2} \)

3. 170.5 km
- Scientific notation: \( 1.705 \times 10^2 \)
- Answer: \( 1.705 \times 10^2 \)

4. 5000 cm³
- Scientific notation: \( 5.000 \times 10^3 \) (Assuming all zeros are significant based on context.)
- Answer: \( 5.000 \times 10^3 \)

5. 36 kg
- Scientific notation: \( 3.6 \times 10^1 \)
- Answer: \( 3.6 \times 10^1 \)

---

#### C. Round off the following measurements to the indicated number of significant digits.

1. 10100 mm (2 significant digits)
- Rounded: \( 10000 \) mm or \( 1.0 \times 10^4 \) mm
- Answer: \( 1.0 \times 10^4 \) mm

2. 0.087400 cL (3 significant digits)
- Rounded: \( 0.0874 \) cL or \( 8.74 \times 10^{-2} \) cL
- Answer: \( 8.74 \times 10^{-2} \) cL

3. 36 kg (1 significant digit)
- Rounded: \( 40 \) kg or \( 4 \times 10^1 \) kg
- Answer: \( 4 \times 10^1 \) kg

4. 2.5689 × 10⁻² s (4 significant digits)
- Rounded: \( 2.569 \times 10^{-2} \) s
- Answer: \( 2.569 \times 10^{-2} \) s

5. 5.920 × 10⁻¹ A (3 significant digits)
- Rounded: \( 5.92 \times 10^{-1} \) A
- Answer: \( 5.92 \times 10^{-1} \) A

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#### D. Perform the following operations.

1. (0.17362 m)(31.22 m)(170.06 m)
- Calculation:
\[
0.17362 \times 31.22 \times 170.06 = 927.09 \, \text{m}^3
\]
- Significant figures: The least precise measurement has 4 significant digits.
- Answer: \( 927.1 \, \text{m}^3 \)

2. \(\frac{9.042 \, \text{g}}{(5.24 \, \text{cm})(9.5 \, \text{cm})}\)
- Calculation:
\[
\text{Denominator: } 5.24 \times 9.5 = 49.78 \, \text{cm}^2
\]
\[
\text{Result: } \frac{9.042}{49.78} = 0.1816 \, \text{g/cm}^2
\]
- Significant figures: The least precise measurement has 3 significant digits.
- Answer: \( 0.182 \, \text{g/cm}^2 \)

3. \(3.500 \times 10^{-2} \, \text{s} + 4.24 \times 10^{-2} \, \text{s}\)
- Calculation:
\[
3.500 \times 10^{-2} + 4.24 \times 10^{-2} = 7.740 \times 10^{-2} \, \text{s}
\]
- Significant figures: The result should have the same number of decimal places as the least precise measurement.
- Answer: \( 7.740 \times 10^{-2} \, \text{s} \)

4. \(\frac{(36 \, \text{kg} - 12.5 \, \text{kg})}{(80.2 \, \text{m}^2 + 12 \, \text{m}^2)}\)
- Calculation:
\[
\text{Numerator: } 36 - 12.5 = 23.5 \, \text{kg}
\]
\[
\text{Denominator: } 80.2 + 12 = 92.2 \, \text{m}^2
\]
\[
\text{Result: } \frac{23.5}{92.2} = 0.255 \, \text{kg/m}^2
\]
- Significant figures: The least precise measurement has 3 significant digits.
- Answer: \( 0.255 \, \text{kg/m}^2 \)

5. \(\frac{7.50 \times 10^2 \, \text{mg} + 1.00 \times 10^3 \, \text{mg}}{3.0 \times 10^1 \, \text{cm} + 4.5 \times 10^2 \, \text{cm}}\)
- Calculation:
\[
\text{Numerator: } 7.50 \times 10^2 + 1.00 \times 10^3 = 1750 \, \text{mg}
\]
\[
\text{Denominator: } 3.0 \times 10^1 + 4.5 \times 10^2 = 480 \, \text{cm}
\]
\[
\text{Result: } \frac{1750}{480} = 3.6458 \, \text{mg/cm}
\]
- Significant figures: The least precise measurement has 2 significant digits.
- Answer: \( 3.6 \, \text{mg/cm} \)

---

Final Answers:

A.
1. 4
2. 5
3. 4
4. 1
5. 2
6. 4
7. 3
8. 3
9. 1
10. 4

B.
1. \( 1.0100 \times 10^4 \)
2. \( 8.7400 \times 10^{-2} \)
3. \( 1.705 \times 10^2 \)
4. \( 5.000 \times 10^3 \)
5. \( 3.6 \times 10^1 \)

C.
1. \( 1.0 \times 10^4 \) mm
2. \( 8.74 \times 10^{-2} \) cL
3. \( 4 \times 10^1 \) kg
4. \( 2.569 \times 10^{-2} \) s
5. \( 5.92 \times 10^{-1} \) A

D.
1. \( 927.1 \, \text{m}^3 \)
2. \( 0.182 \, \text{g/cm}^2 \)
3. \( 7.740 \times 10^{-2} \, \text{s} \)
4. \( 0.255 \, \text{kg/m}^2 \)
5. \( 3.6 \, \text{mg/cm} \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{A. } 4, 5, 4, 1, 2, 4, 3, 3, 1, 4 \\
\text{B. } 1.0100 \times 10^4, 8.7400 \times 10^{-2}, 1.705 \times 10^2, 5.000 \times 10^3, 3.6 \times 10^1 \\
\text{C. } 1.0 \times 10^4 \, \text{mm}, 8.74 \times 10^{-2} \, \text{cL}, 4 \times 10^1 \, \text{kg}, 2.569 \times 10^{-2} \, \text{s}, 5.92 \times 10^{-1} \, \text{A} \\
\text{D. } 927.1 \, \text{m}^3, 0.182 \, \text{g/cm}^2, 7.740 \times 10^{-2} \, \text{s}, 0.255 \, \text{kg/m}^2, 3.6 \, \text{mg/cm}
\end{array}
}
\]