Signifikante Stellen – Zählen und Runden
Zähle signifikante Stellen in einer Zahl und runde auf N signifikante Stellen.
What are Significant Figures?
Significant figures (sig figs) are the meaningful digits in a measurement. They indicate the precision of a value. Rules for counting sig figs:
- All non-zero digits are significant (e.g., 123 has 3 sig figs)
- Zeros between non-zero digits are significant (e.g., 1001 has 4 sig figs)
- Leading zeros are NOT significant (e.g., 0.005 has 1 sig fig)
- Trailing zeros after a decimal point ARE significant (e.g., 1.500 has 4 sig figs)
- Trailing zeros without a decimal point are ambiguous (e.g., 100 might have 1, 2, or 3 sig figs)
How to Round to Significant Figures
To round 0.004567 to 3 significant figures:
- Identify the first significant figure: 4 (the leading zeros don't count)
- Count 3 significant figures from there: 4, 5, 6
- Look at the next digit (7): since 7 ≥ 5, round up the last kept digit
- Result: 0.00457
When rounding large numbers, use scientific notation to avoid ambiguity. For example, 12,345 rounded to 3 sig figs = 1.23 × 10⁴ = 12,300.
Sig Figs in Calculations
When performing calculations, the result should be rounded to match the precision of the least precise input:
- Multiplication/Division: The result has as many sig figs as the input with the fewest sig figs. 2.1 × 3.45 = 7.245, rounded to 2 sig figs = 7.2
- Addition/Subtraction: The result has as many decimal places as the input with the fewest decimal places. 1.23 + 4.1 = 5.33, rounded to 1 decimal = 5.3
Häufig gestellte Fragen
How many sig figs does 0.00450 have?
0.00450 has 3 significant figures: 4, 5, and 0. The leading zeros are not significant (they are place holders), but the trailing zero after 5 IS significant because it follows a non-zero digit after a decimal point.
Are trailing zeros significant?
Trailing zeros are significant if they appear after a decimal point (e.g., 2.500 has 4 sig figs). Without a decimal point, trailing zeros are ambiguous (e.g., 2500 could have 2, 3, or 4 sig figs). Scientific notation eliminates this ambiguity: 2.5 × 10³ clearly has 2 sig figs.
Why do sig figs matter in science?
Sig figs communicate the precision of a measurement. Reporting more sig figs than your instrument can measure implies false precision. For example, measuring a pencil with a ruler marked in mm and reporting 14.2345 cm is misleading — you can only reliably claim 14.2 cm (3 sig figs).