Besaran, Satuan, Dimensi, dan Pengukuran • Part 5: Angka Penting

Introduction

This tutorial provides a comprehensive overview of significant figures, also known as angka penting, which are crucial in measurements and calculations. Understanding significant figures helps ensure accuracy and precision in scientific work. This guide will walk you through the definition, rules for determining significant figures, and how to apply these rules in calculations.

Step 1: Understand the Concept of Significant Figures

• Significant figures are the digits in a number that contribute to its precision.
• This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal part.
• Example: In the number 0.00452, the significant figures are 4, 5, and 2 (3 significant figures).

Step 2: Learn the Rules for Determining Significant Figures

1. Non-zero digits are always significant.
2. Any zeros between significant figures are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros in a decimal number are significant.
5. Trailing zeros in a whole number without a decimal point are not significant.

Step 3: Practice Determining Significant Figures

• Review the following examples:
  • 123 has 3 significant figures.
  • 0.00456 has 3 significant figures.
  • 1500 has 2 significant figures (unless specified with a decimal as in 1500. which has 4).
  • 0.0700 has 3 significant figures.

Step 4: Apply Significant Figures in Calculations

• When performing calculations, the result should have a number of significant figures based on the least precise measurement.

Addition and Subtraction

• The result should be rounded to the least number of decimal places of any number in the calculation.
  • Example: 12.11 (2 decimal places) + 0.3 (1 decimal place) = 12.41 → rounded to 12.4.

Multiplication and Division

• The result should have the same number of significant figures as the measurement with the least number of significant figures.
  • Example: 4.56 (3 significant figures) × 1.4 (2 significant figures) = 6.384 → rounded to 6.4.

Step 5: Work Through Examples

Example 1: Determine Significant Figures

• Find the number of significant figures in 0.004500:
  • Answer: 4 significant figures (the zeros after 45 are significant).

Example 2: Perform Operations with Significant Figures

• Calculate 5.67 + 2.0:
  • Answer: 7.7 (rounded to one decimal place).

Example 3: Solve a Word Problem

• If you measure the length of a table as 2.50 m and the width as 1.2 m, what is the area?
  • Calculate area = length × width = 2.50 m × 1.2 m = 3.0 m² (rounded to two significant figures).

Conclusion

Understanding significant figures is essential for accurate measurement and reporting in scientific contexts. By applying the rules and practicing with examples, you can enhance your precision in calculations. As a next step, consider exploring more complex measurement topics or practice with additional examples to solidify your understanding.