Concept explainers
1.43 Calculate the following to the correct number of significant figures. Assume that all these numbers are measurements.
(a)
(b)
(c)
(d)
(a)
To perform: The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant
- zeroes to the right are not significant if not specified as “exact” zeroes
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant
Second, define the addition/subtraction and multiplication/division rules for significant numbers
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation.
We must keep only 1 significant figure after the decimal. Round if required
(b)
To perform: The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant
- zeroes to the right are not significant if not specified as “exact” zeroes
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant
Second, define the addition/subtraction and multiplication/division rules for significant numbers
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation. Substitute
According to the rules, we must keep the number with the least sig. fig. This is 17.10, with only 4 significant figure then
(c)
To perform: The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant
- zeroes to the right are not significant if not specified as “exact” zeroes
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant
Second, define the addition/subtraction and multiplication/division rules for significant numbers
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation. Perform calculation
The significant figures are given as:
We must keep the smallest amount of sig. fig. for multiplication, therefore, choose 5.
(d)
To perform: The calculations of
Explanation of Solution
First, set the rules for “significant numbers”
- zeroes to the left are not significant
- zeroes to the right are not significant if not specified as “exact” zeroes
- all other digits other than zero are significant.
- zeroes between non-zero numbers are significant
Second, define the addition/subtraction and multiplication/division rules for significant numbers
- Addition/Subtraction ( Always keep the least significant number after the decimal point.
- Multiplication/Division ( Always keep the least significant number of the whole number.
- If addition/subtraction and Multiplication/division are included, separate the operation to simple operations and keep following the rules.
Now, for the given operation. Perform calculation
For the inside addition, keep only 1 significant figure after the digit, since 0.12 has 2 significant figures after the digit and 25.2 has only 1.
When performing the inside of the square root
Then, continue with the division. Keep the least amount of significant figures in total.
Now, add all.
Keep the least amount of significant figures after the decimal point. Which is 4 for both amounts.
Always ensure to keep the correct significant numbers when performing addition, subtraction, multiplication and division. It is relevant to keep track of accuracy in the measurements.
Want to see more full solutions like this?
Chapter 1 Solutions
Chemistry for Engineering Students
- 1-85 In Japan, high-speed “bullet trains” move with an average speed of 220. km./h. If Dallas and Los Angeles were connected by such a train, how long would it take to travel nonstop between these cities (a distance of 1490. miles)?arrow_forward1-76 If the density of air is 1.25 10-3 g/cc, what is the mass in kilograms of the air in a room that is 5.3 m long, 4.2 m wide, and 2.0 m high?arrow_forward1-78 The kinetic energy possessed by an object with a mass of 1 g moving with a velocity of 1 cm/s is called 1 erg. What is the kinetic energy, in ergs, of an athlete with a mass of 127 lb running at a velocity of 14.7 mi/h?arrow_forward
- A student is given the following question:"What is the mass of a gold bar that is 7.379 × 10–4 m3 in volume? The density of gold is 19.3 g/cm3."The student obtains the answer through the following calculation: For the above calculation, how many significant figures should you report the answer to?arrow_forward1-98 The antifreeze-coolant compound used in cars does not have the same density as water. Would a hydrometer be useful for measuring the amount of antifreeze in the cooling system?arrow_forward1-65 While you drive your car, your battery is being charged. How would you describe this process in terms of kinetic and potential energy?arrow_forward
- 1-91 In calculating the specific heat of a substance, the following data are used: mass = 92.15 g; heat = 3.200 kcal; rise in temperature = 45oC. How many significant figures should you report in calculating the specific heat?arrow_forward1-86 The specific heats of some elements at 25oC are as follows: aluminum = 0.215 cal/g · oC; carbon (graphite) = 0.170 caI/g oC; iron = 0.107 cal/g mercury = 0.033 1 caI/g oC. (a) Which element would require the smallest amount of heat to raise the temperature of 100 g of the element by 10oC? (b) If the same amount of heat needed to raise the temperature of 1 g of aluminum by 25oC were applied to 1 g of mercury, by how many degrees would its temperature be raised? (c) If a certain amount of heat is used to raise the temperature of 1.6 g of iron by 10oC, the temperature of 1 g of which element would also be raised by 10oC, using the same amount of heat?arrow_forward1-67 If 168 g of an unknown liquid requires 2750 cal of heat to raise its temperature from 26oC to 74oC, what is the specific heat of the liquid?arrow_forward
- 1-31 In the SI system, the second is the base unit of time. We talk about atomic events that occur in picoseconds (10-12 s) or even in femtoseconds (10-15 s). But we don’t talk about megaseconds or kiloseconds; the old standards of minutes, hours, and days prevail. How many minutes and hours are 20. kiloseconds?arrow_forward1-51 A nurse practitioner orders isotonic sodium lactate 50. mL/kg body mass to be administered intravenously for a 139-lb patient with severe acidosis. The rate of flow is 150 gtts/min, and the IV administration set delivers 20. gtts/mL, where the unit “gtts” stands for drops of liquid. What is the running time in minutes?arrow_forward1-77 Classify these as kinetic or potential energy: (a) Water held by a dam (b) A speeding train (c) A book on its edge before falling (d) A falling book (e) Electric current in a lightbulbarrow_forward
- Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningIntroduction to General, Organic and BiochemistryChemistryISBN:9781285869759Author:Frederick A. Bettelheim, William H. Brown, Mary K. Campbell, Shawn O. Farrell, Omar TorresPublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning
- Chemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningGeneral Chemistry - Standalone book (MindTap Cour...ChemistryISBN:9781305580343Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; DarrellPublisher:Cengage Learning