Messung und signifikante Stellen – Probleme und Lösungen
1. Die Länge eines Objekts, gemessen mit einem Mikrometer beträgt 15.08 mmBestimmen Sie die bedeutende Figuren und die Anzahl der signifikanten Stellen.
A. 15.08 mm und drei bedeutende Figuren
B. 1.508 mm und vier bedeutende Figuren
C. 15.08 mm und vier bedeutende Figuren
D. 1.508 mm und drei bedeutende Figuren
Lösung:
Significant figures = 15.08 mm
The number of significant figures = 4
Die richtige Antwort ist C.
2. A student measures the volume of a container using a small cup with a volume of 125 cm3. The container is full after filled with twenty-half cups. Determine the volume of container based on significant figure rules.
A. 2562.5 cm3
B. 2.56 x 103 cm3
Ca. 2563 cm3
D. 2.56 x 10-3 m3
Lösung:
Volume of a cup = 125 cm3
Volume of container = 20.5 x 125 cm3 = 2562.5 cm3
Die richtige Antwort ist A.
3. Determine the result of measuring an object as shown in figure below, according to the rules of significant figures.
A. 4.5 mm
B. 4.6 mm
C. 4.6 mm
D. 4.6 mm
Lösung:
Main scale = 4.5 mm
Second scale = 11 x 0.01 mm = 0.1 mm (according to the rules of the multiplication of significant figures)
The result of measuring = 4.5 mm + 0.1 mm = 4.6 mm (according to the rules of the summing of significant figures)
Die richtige Antwort ist C.
1. Problem: Round 27.6891 to four significant figures.
Lösung: 27.69 (because 1 doesn’t affect the third decimal place).
2. Problem: If you multiply 6.34 (3 significant figures) by 5.678 (4 significant figures), how many significant figures should your answer have?
Lösung: The answer should have 3 significant figures.
3. Problem: A scientist recorded a result of 5001 grams. How many significant figures does this value have?
Lösung: 4 significant figures.
4. Problem: What is the result when you add 24.5 (3 significant figures) and 1.789 (4 significant figures)?
Lösung: The sum is 26.289, but considering significant figures, you should round to 26.3.
5. Problem: If a physics experiment gives a speed of 0.0056078 m/s, how many significant figures are there?
Lösung: 5 significant figures.
6. Problem: Round 0.007809 to four significant figures.
Lösung: 0.007809 (because it already has four significant figures).
7. Problem: When measuring the depth of a well, you get a value of 78.00 meters. Later, another reading says 78.0001 meters. If you average the values, how many significant figures should your answer have?
Lösung: The average should have 4 significant figures. Thus, 78.00 + = 78.00012 78.00005 wird 78.00.
8. Problem: You measure the width of a book as 150 mm. How many significant figures are there?
Lösung: 2 significant figures.
9. Problem: What is the result when you divide 90.12 (4 significant figures) by 4.0 (2 significant figures)?
Lösung: The result is 22.53, but considering significant figures, the answer should be rounded to 23.
10. Problem: You measure 0.4000 liters of liquid A and 0.4020 liters of liquid B. When reporting the total volume, to how many decimal places should you report your answer?
Lösung: You should round to 4 decimal places. Thus, 0.4000 + = 0.4020 0.8020.
11. Problem: Round 50.0012 to five significant figures.
Lösung: 50.001 (because 2 doesn’t affect the fourth decimal place).
12. Problem: When subtracting 45.67 (4 significant figures) from 100.1 (4 significant figures), how many significant figures should your answer have?
Lösung: The answer should have 4 significant figures. So, 100.1 – 45.67 = 54.43.
13. Problem: A result was documented as 1020 with no decimal point. How many significant figures does this have?
Lösung: 3 significant figures.
14. Problem: What’s the result when you subtract 2.3456 (5 significant figures) from 5.00 (3 significant figures)?
Lösung: The result is 2.6544, but considering significant figures, you should round to 2.65.
15. Problem: Wie viele signifikante Ziffern enthält die Zahl 0.005002?
Lösung: 4 significant figures.
16. Problem: Round 10.4987 to three significant figures.
Lösung: 10.5
17. Problem: You get a voltage reading of 50.00 V from one instrument and 50.0005 V from another. If you average the readings, how many significant figures should the result have?
Lösung: The average should have 4 significant figures. So, 50.00 + = 50.00052 50.00025 wird 50.00.
18. Problem: The length of a rod is measured to be 200 mm. How many significant figures does this measurement have?
Lösung: 1 significant figure.
19. Problem: You’re dividing 4.56 (3 significant figures) by 2.0 (2 significant figures). What should be the number of significant figures in the answer?
Lösung: The answer should have 2 significant figures. So, 4.56 ÷ 2.0 = 2.28.
20. Problem: The measured distance between two towns is 100.50 km. How many significant figures does this measurement have?
Lösung: 5 significant figures.
