Concept explainers
(a)
Interpretation:
The following calculation is to be solved to the correct number of significant figures.
Concept introduction:
Significant figures of a number are the digits which carry meaningful contribution to its measurement resolution. The rightmost digit of the quantity is the most uncertain digit. The number of certain and uncertain digit in a quantity is considered as significant figures. The digit with a higher number of significant figures has a higher certainty of measurement.
To determine the number of significant figures in a quantity following steps is followed.
1. The quantity must has a decimal point.
2. Start counting from the left and proceed towards the right until the first nonzero digit is encountered. All nonzero digit and the zeroes between two nonzero digits are considered as significant figures. For example, 0.0000765 has three significant figures and 7009 has four significant figures.
3. Zeroes after a decimal point are significant figures. For example, 42.0 have three significant figures.
4. Trailing zeroes that do nothing but are used to set a decimal point are non-significant figures. However, exponential notation can be used to avoid confusion. For example, 4300 has 3 significant figures. It can be expressed in scientific notation as
5. Zeroes present before a trailing decimal point are significant figures. For example, 3200 has only two significant figures but 3200. has 4 significant figures.
Rules to determine significant figures in calculations are as follows:
(1) In multiplication and division operations the result carries the same number of significant figures as the operand or measurement with the fewest significant figures.
(2) In addition and subtraction operations, the result carries the same number of decimal places as the operand or measurement with fewest decimal places.
(3) Exact numbers do not affect the number of significant digits in the final answer.
In mathematical expression which involves mixed operations the result of each intermediate step with proper significant figures. Avoid rounding of the result at intermediate steps. Round off the final answer of the calculation. The rules to round off are as follows:
(1) If the last dropped digit is greater than 5 then increase the preceding digit by 1.
(2) If the last dropped digit is less than 5 then the preceding digit does not change.
(3) If the last digit dropped is 5, then the preceding digit is increased by 1 if it is odd and remains the same if it is even. Also, if 5 is followed by zeroes only then rule (3) is applicable and if it is followed by non-zero digit then rule (1) is applicable.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 1.59P
The answer of the calculation to a correct number of significant figures is
Explanation of Solution
The given expression is,
The least significant digit in each number is underlined as follows:
Add
The result of the addition operation must carry the same number of decimal places as the measurement with fewest decimal places. Measurement
Divide
The result of the division operation must carry the same number of significant figures as the measurement with the fewest significant figures.
The last digit to be dropped is 5 and the preceding digit is odd thus it is increased by 1.
The final answer is rounded off to 2 significant figures. The answer of the calculation to a correct number of significant figures is
(b)
Interpretation:
The following calculation is to be solved to the correct number of significant figures.
Concept introduction:
Significant figures of a number are the digits which carry meaningful contribution to its measurement resolution. The rightmost digit of the quantity is the most uncertain digit.
The number of certain and uncertain digit in a quantity is considered as significant figures. The digit with a higher number of significant figures has a higher certainty of measurement.
To determine the number of significant figures in a quantity following steps is followed.
1. The quantity must has a decimal point.
2. Start counting from the left and proceed towards the right until the first nonzero digit is encountered. All nonzero digit and the zeroes between two nonzero digits are considered as significant figures. For example, 0.0000765 has three significant figures and 7009 has four significant figures.
3. Zeroes after a decimal point are significant figures. For example, 42.0 have three significant figures.
4. Trailing zeroes that do nothing but are used to set a decimal point are non-significant figures. However, exponential notation can be used to avoid confusion. For example, 4300 has 3 significant figures. It can be expressed in scientific notation as
5. Zeroes present before a trailing decimal point are significant figures. For example, 3200 has only two significant figures but 3200. has 4 significant figures.
Rules to determine significant figures in calculations are as follows:
(1) In multiplication and division operations the result carries the same number of significant figures as the operand or measurement with the fewest significant figures.
(2) In addition and subtraction operations, the result carries the same number of decimal places as the operand or measurement with fewest decimal places.
(3) Exact numbers do not affect the number of significant digits in the final answer.
In mathematical expression which involves mixed operations the result of each intermediate step with proper significant figures. Avoid rounding of the result at intermediate steps. Round off the final answer of the calculation. The rules to round off are as follows:
(1) If the last dropped digit is greater than 5 then increase the preceding digit by 1.
(2) If the last dropped digit is less than 5 then the preceding digit does not change.
(3) If the last digit dropped is 5, then the preceding digit is increased by 1 if it is odd and remains the same if it is even. Also, if 5 is followed by zeroes only then rule (3) is applicable and if it is followed by non-zero digit then rule (1) is applicable.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 1.59P
The answer of the calculation to a correct number of significant figures is
Explanation of Solution
The given expression is,
The least significant digit in each number is underlined as follows:
Subtract
The result of the subtraction operation must carry the same number of decimal places as the measurement with fewest decimal places. Measurement
Divide
The result of the division operation must carry the same number of significant figures as the measurement with the fewest significant figures.
The final answer is rounded off to 2 significant figures. The answer of the calculation to a correct number of significant figures is
(c)
Interpretation:
The following calculation is to be solved to the correct number of significant figures.
Concept introduction:
Significant figures of a number are the digits which carry meaningful contribution to its measurement resolution. The rightmost digit of the quantity is the most uncertain digit.
The number of certain and uncertain digit in a quantity is considered as significant figures. The digit with a higher number of significant figures has a higher certainty of measurement.
To determine the number of significant figures in a quantity following steps is followed.
1. The quantity must has a decimal point.
2. Start counting from the left and proceed towards the right until the first nonzero digit is encountered. All nonzero digit and the zeroes between two nonzero digits are considered as significant figures. For example, 0.0000765 has three significant figures and 7009 has four significant figures.
3. Zeroes after a decimal point are significant figures. For example, 42.0 have three significant figures.
4. Trailing zeroes that do nothing but are used to set a decimal point are non-significant figures. However, exponential notation can be used to avoid confusion. For example, 4300 has 3 significant figures. It can be expressed in scientific notation as
5. Zeroes present before a trailing decimal point are significant figures. For example, 3200 has only two significant figures but 3200. has 4 significant figures.
Rules to determine significant figures in calculations are as follows:
(1) In multiplication and division operations the result carries the same number of significant figures as the operand or measurement with the fewest significant figures.
(2) In addition and subtraction operations, the result carries the same number of decimal places as the operand or measurement with fewest decimal places.
(3) Exact numbers do not affect the number of significant digits in the final answer.
In mathematical expression which involves mixed operations the result of each intermediate step with proper significant figures. Avoid rounding of the result at intermediate steps. Round off the final answer of the calculation. The rules to round off are as follows:
(1) If the last dropped digit is greater than 5 then increase the preceding digit by 1.
(2) If the last dropped digit is less than 5 then the preceding digit does not change.
(3) If the last digit dropped is 5, then the preceding digit is increased by 1 if it is odd and remains the same if it is even. Also, if 5 is followed by zeroes only then rule (3) is applicable and if it is followed by non-zero digit then rule (1) is applicable.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 1.59P
The answer of the calculation to a correct number of significant figures is
Explanation of Solution
The value of
The formula to calculate the volume is,
Substitute
The result of the multiplication and division operation must carry the same number of significant figures as the measurement with the fewest significant figures.
The final answer is rounded off to 3 significant figures. The answer of the calculation to a correct number of significant figures is
Want to see more full solutions like this?
Chapter 1 Solutions
CHEM 212:CHEMISTSRY V 2
- Explain the term “inductively coupled plasma.”arrow_forwardUsing Pauling electronegativity values and a Ketelaar triangle, what type of compound is brass, a CuZn alloy? Group of answer choices metallic ionic covalentarrow_forwardChallenging samples: 1. Metal complexes with low volatility are often difficult to analyze when performing atomic absorption measurements because the atomization efficiency is reduced to unacceptably low levels. Devise a strategy or strategies for eliminating the problem of a non-volatile metal complex? Explain how you would do that. 2. Devise a strategy to overcome unwanted ionization of the analyte? Explain what it would be. 3. Devise a general method that can be used to account for the presence of unknown matrix effects.arrow_forward
- Don't used hand raitingarrow_forwardDon't used hand raiting don't used Ai solutionarrow_forwardHomework: Atomic Structure This homework is due at the beginning of class next lecture period and is worth 6 points. Please place the number of protons and neutrons in the nucleus and then put the number of electrons in the correct shell. Also give the correct atomic mass. Also, state if the atom is an ion (cation or anion). H* 1. Number of protons Number of electrons Number of neutrons Atomic mass 2. 26 13AI +++ Number of protons Number of neutrons Number of electrons Atomic massarrow_forward
- Don't used Ai solution and don't used hand raitingarrow_forward& Calculate the molar enthalpy of combustion (A combH) of 1.80 g of pyruvic acid (CH3COCOOH; 88.1 g mol-1) at 37 °C when they are combusted in a calorimeter at constant volume with a calorimeter constant = 1.62 kJ °C-1 and the temperature rose by 1.55 °C. Given: R = 8.314 J mol −1 °C-1 and the combustion reaction: AN C3H4O3 + 2.502(g) → 3CO2(g) + 2H2O(l)arrow_forwardAn unknown salt, AB, has the following precipitation reaction:A+(aq) + B-(aq) ⇌ AB(s) the K value for this reaction is 4.50 x10-6. Draw a model that represents what will happen when 1.00 L each of 1.00 M solution of A+(aq) and 1.00M solution of B-(aq) are combined.arrow_forward
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill EducationPrinciples of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning
- Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill EducationChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningElementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305957404/9781305957404_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781259911156/9781259911156_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305577213/9781305577213_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780078021558/9780078021558_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305079373/9781305079373_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781118431221/9781118431221_smallCoverImage.gif)