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

Definition of Significant Figures (Angka Penting)
📌 Significant figures are digits obtained from a measurement, consisting of exact (certain) digits and estimated (uncertain/doubtful) digits.
📏 For example, when measuring a book's thickness with a ruler (precision of 0.1 cm), if the reading is between 1.4 cm and 1.5 cm, an observer might record 1.48 cm; here, 1.4 is the certain part, and 8 is the estimated digit.
🔬 The estimated digit (the last digit) arises from the subjectivity of the observer due to the limitations of the measuring instrument's precision.

Rules for Determining Significant Figures
🔢 All non-zero digits are significant (e.g., 2537 has 4 significant figures).
🎯 Zeros located between non-zero digits are significant (e.g., 50025 has 5 significant figures, 5002 has 4 significant figures).
📉 Zeros to the left of the first non-zero digit are not significant (e.g., 0.0032 has 2 significant figures: 3 and 2).
🔟 Zeros to the right of the last non-zero digit are significant *only if* a decimal point is present (e.g., 12.750 has 5 significant figures; 200 has 1 significant figure, but 200.00 has 5 significant figures).
✍️ In scientific notation ($a \times 10^n$), only the digits in the coefficient ($a$) are considered significant; the $10^n$ term is ignored for counting significant figures.

Operations Involving Significant Figures
➕➖ Addition and Subtraction: The result must be rounded to have the same number of decimal places as the measurement with the fewest decimal places.
✖️➗ Multiplication and Division: The result must be rounded to have the same number of significant figures as the measurement with the fewest significant figures.
📈 Powers and Roots (Exponentiation/Radicals): The result must have the same number of significant figures as the original number before the operation.

Application Examples
📐 For multiplication (Area = Length $\times$ Width), if Length (12.5 cm, 3 SF) is multiplied by Width (7.5 cm, 2 SF), the result must be limited to 2 significant figures.
$12.5 \times 7.5 = 93.75 \rightarrow 94 \text{ cm}^2$ (rounded to 2 SF).
🧱 For repeated addition (Height of 35 stacks of bricks, where one brick height is 9.10 cm, 3 SF), the multiplier (35) is not considered a significant figure because it is a count, not a measurement. The result (318.5 cm) must be rounded to 3 significant figures $\rightarrow 319 \text{ cm}$.

Key Points & Insights
➡️ The estimated digit is the rightmost digit in any measurement and reflects the precision limit of the tool used.
➡️ For addition/subtraction, focus on decimal places; for multiplication/division, focus on the total count of significant figures.
➡️ Integers used as counters (like the number of stacked items) are not subject to significant figure rules unless they result from a measurement process.

📸 Video summarized with SummaryTube.com on Nov 09, 2025, 11:44 UTC