Q. What is the correct way to express 0.0001234 in scientific notation with significant figures?
A.
1.234 x 10^-4
B.
1.23 x 10^-4
C.
1.2340 x 10^-4
D.
1.2 x 10^-4
Solution
In scientific notation, all non-zero digits are significant. Therefore, 0.0001234 can be expressed as 1.234 x 10^-4, maintaining all significant figures.
Q. What is the correct way to express 0.000345 in scientific notation with significant figures?
A.
3.45 x 10^-4
B.
3.450 x 10^-4
C.
3.4500 x 10^-4
D.
3.4 x 10^-4
Solution
In scientific notation, all digits in the coefficient are significant. Therefore, 0.000345 is expressed as 3.45 x 10^-4, which has 3 significant figures.
Q. What is the product of 3.00 and 2.5, considering significant figures?
A.
7.5
B.
7.50
C.
7.500
D.
7.55
Solution
In multiplication, the result should have the same number of significant figures as the factor with the least significant figures. 3.00 has 3 significant figures and 2.5 has 2 significant figures, so the result should have 2 significant figures: 7.5.
Q. What is the result of 5.00 - 2.1, considering significant figures?
A.
2.90
B.
2.9
C.
2.8
D.
2.80
Solution
When subtracting, the result should be rounded to the least number of decimal places. 5.00 has two decimal places and 2.1 has one, so the result should be rounded to one decimal place: 5.00 - 2.1 = 2.90 becomes 2.9.
Q. What is the result of adding 12.11 and 0.3, considering significant figures?
A.
12.41
B.
12.4
C.
12.5
D.
12.3
Solution
When adding, the result should be rounded to the least number of decimal places. 12.11 has two decimal places and 0.3 has one, so the result should be rounded to one decimal place: 12.41 becomes 12.4.
Q. What is the result of dividing 100.0 by 4.00, considering significant figures?
A.
25.0
B.
25
C.
25.00
D.
24.99
Solution
In division, the result should have the same number of significant figures as the measurement with the least significant figures. 100.0 has 4 significant figures and 4.00 has 3 significant figures, so the answer should be 25.0 with 3 significant figures.
Q. What is the result of dividing 6.38 by 2.0, considering significant figures?
A.
3.19
B.
3.2
C.
3.0
D.
3.5
Solution
In division, the result should have the same number of significant figures as the measurement with the least significant figures. 6.38 has 3 significant figures and 2.0 has 2 significant figures, so the answer should be rounded to 2 significant figures: 3.19 becomes 3.2.
Q. What is the result of dividing 8.0 by 2.00, considering significant figures?
A.
4.0
B.
4
C.
4.00
D.
4.000
Solution
In division, the result should have the same number of significant figures as the measurement with the least significant figures. 8.0 has 2 significant figures and 2.00 has 3 significant figures, so the answer should be 4.0 (2 significant figures).
Q. What is the result of multiplying 6.02 x 10^23 by 3.0, considering significant figures?
A.
1.8 x 10^24
B.
1.806 x 10^24
C.
1.80 x 10^24
D.
1.8060 x 10^24
Solution
In multiplication, the result should have the same number of significant figures as the factor with the least significant figures. 6.02 x 10^23 has 3 significant figures and 3.0 has 2, so the answer should be 1.8 x 10^24.
Q. What is the result of subtracting 5.00 from 10.0, considering significant figures?
A.
5.0
B.
5
C.
5.00
D.
5.000
Solution
In subtraction, the result should be rounded to the least number of decimal places. 10.0 has one decimal place and 5.00 has two, so the result should be rounded to one decimal place: 5.0.
Q. What is the result of subtracting 5.678 from 10.0, considering significant figures?
A.
4.32
B.
4.3
C.
4.4
D.
4.00
Solution
In subtraction, the result should be rounded to the least number of decimal places. 10.0 has one decimal place and 5.678 has three, so the result should be rounded to one decimal place: 4.32 becomes 4.3.
Q. When dividing 100.0 by 4.00, what is the correct answer considering significant figures?
A.
25.0
B.
25
C.
25.00
D.
24.99
Solution
In division, the result should have the same number of significant figures as the quantity with the least significant figures. 100.0 has 4 significant figures and 4.00 has 3 significant figures, so the result should have 3 significant figures: 25.0.
Q. When dividing 6.02 by 2.0, how many significant figures should the answer have?
A.
1
B.
2
C.
3
D.
4
Solution
The result should have the same number of significant figures as the measurement with the least significant figures, which is 2.0 (1 significant figure).
Q. When dividing 6.022 x 10^23 by 2.0, how many significant figures should the answer have?
A.
1
B.
2
C.
3
D.
4
Solution
In division, the result should have the same number of significant figures as the factor with the least significant figures. 6.022 x 10^23 has 4 significant figures and 2.0 has 2 significant figures, so the answer should have 2 significant figures.
Understanding significant figures is crucial for students preparing for exams, as it directly impacts the accuracy of numerical answers. Practicing MCQs and objective questions on significant figures helps reinforce this concept, ensuring you can tackle important questions with confidence. By mastering significant figures, you enhance your exam preparation and improve your overall performance in both school and competitive exams.
What You Will Practise Here
Definition and importance of significant figures in scientific calculations.
Rules for determining significant figures in different types of numbers.
How to perform calculations involving significant figures, including addition, subtraction, multiplication, and division.
Common examples and practice questions to solidify your understanding.
Identifying significant figures in measurements and their implications.
Application of significant figures in real-world scenarios and experiments.
Tips and tricks for quickly identifying significant figures in MCQs.
Exam Relevance
Significant figures are a key topic in various examinations, including CBSE, State Boards, NEET, and JEE. Questions often focus on identifying significant figures in given numbers, performing calculations while maintaining the correct number of significant figures, and interpreting results in the context of scientific data. Familiarity with this topic can help you tackle both direct and application-based questions effectively.
Common Mistakes Students Make
Confusing leading zeros with significant figures, often miscounting them.
Neglecting to adjust the number of significant figures in calculations, leading to incorrect answers.
Overlooking the rules for significant figures in multiplication and division compared to addition and subtraction.
Failing to recognize that trailing zeros in a whole number without a decimal point are not significant.
FAQs
Question: What are significant figures? Answer: Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion.
Question: How do I determine the number of significant figures in a measurement? Answer: Count all non-zero digits, any zeros between them, and any trailing zeros in a decimal number. Leading zeros are not counted.
Ready to enhance your understanding of significant figures? Dive into our practice MCQs and test your knowledge to ensure you are well-prepared for your exams!
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