Solved Examples of Significant Figures in Physics Calculations

📚 Quick Study Guide

• 🔢 Definition: Significant figures are the digits in a number that contribute to its precision.
• 📏 Rules for identifying significant figures:
  • Non-zero digits are always significant.
  • Zeros between non-zero digits are significant.
  • Leading zeros are not significant.
  • Trailing zeros in a number containing a decimal point are significant.
• ➕ Addition/Subtraction: The result should have the same number of decimal places as the number with the fewest decimal places.
• ✖️ Multiplication/Division: The result should have the same number of significant figures as the number with the fewest significant figures.
• 🧪 Exact Numbers: Exact numbers (e.g., conversion factors like 1 m = 100 cm) have infinite significant figures.
• 💡 Rounding: If the digit following the last significant figure is 5 or greater, round up. If it's less than 5, round down.

Practice Quiz

1. What is the number of significant figures in 0.004020?
   1. 3
   2. 4
   3. 5
   4. 7
2. Calculate $2.5 \times 3.15$ and express the answer with the correct number of significant figures.
   1. 7.875
   2. 7.9
   3. 8
   4. 7.88
3. What is the result of $4.25 + 0.328$, expressed with the correct number of significant figures?
   1. 4.578
   2. 4.58
   3. 4.6
   4. 4.57
4. How many significant figures are in the number $1.20 \times 10^3$?
   1. 2
   2. 3
   3. 4
   4. 6
5. A rectangle has a length of 12.5 cm and a width of 4.5 cm. What is the area, expressed with the correct number of significant figures?
   1. 56.25 cm²
   2. 56 cm²
   3. 56.3 cm²
   4. 57 cm²
6. What is the result of $\frac{15.6}{3.0}$, expressed with the correct number of significant figures?
   1. 5.2
   2. 5
   3. 5.20
   4. 5.0
7. What is 10.07 - 0.1 expressed with correct sig figs?
   1. 9.07
   2. 9.1
   3. 9.0
   4. 9