Chapter 3, Problem 113E

Distinguish precisely and in scientific terms the differences among items in each of the following groups.

a) Coefficient, exponent, exponential

b) Equivalency, conversion factor, quantity, value, unit

c) Analyze, identify, construct, check

d) Mass, weight

e) Unit, kilounit, centiunit, milliunit

f) Significant figures, uncertain digit

g) Uncertainty, exact number

h) The symbols = and

i) Fahrenheit, Celsius, kelvin

j) Direct proportionality, proportionality constant

k) Density, mass, volume

Interpretation Introduction

(a)

Interpretation:

To determine the differences among items in each of the given groups is to be stated.

Coefficient, exponent, exponential

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Scientific notation is the way to express the numbers that are too big or small that can be written conveniently in the decimal form. It is commonly used by the scientist, mathematics, to simplify the certain arithmetic operation. In the scientific notation, the numbers are indicated by

M $\times$ 10ⁿ

Answer to Problem 113E

The scientific notation coefficient is denoted as the number equal to or greater than 1 and less than 10. Exponential is given as a power term with base ten. Moreover, exponential is only the power term and it is a whole number, which have positive or negative values.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. It exists in several forms with different choices of the basic units. The metric system features a single base unit for many physical quantities. Other quantities are derived from the SI units.

Scientific notation: a.bcd x 10^e

In scientific notation coefficient is denoted as the number equal to or greater than 1 and less than 10 (a.bcd). Exponential is given as a power term with base ten (10^e). Moreover, exponent is only the power term (e) and it is a whole number, which have positive or negative values.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(b)

Interpretation:

To determine the differences among items in each of the given groups is to be stated.

Equivalency, conversion factor, quantity, value, unit

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

Equivalency is two quantities that are equivalent in value. The fractional value of an equivalency is conversion factor. Quantity is the product of value and product. The numerical denomination is value and the designation associated with value is called unit.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. The metric system features a single base unit for many physical quantities. Equivalency is two quantities that are equivalent in value. The fractional value of an equivalency is conversion factor. Quantity is the product of value and product. The numerical denomination is value and the designation associated with value is called unit.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(c)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Analyze, identify, construct, check

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

Analyze is evaluation of problem statement with the given quantity i.e., the product of value and unit. Identity is the process of collection of equivalencies or an algebraic relationship which are needed to solve the problem. Construct deals with setting up the solution. Check involves solution checkup with the levels of making sense and what was learned.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. The term analyze is evaluation of problem statement with the given quantity i.e., the product of value and unit. Identity is the process of collection of equivalencies or an algebraic relationship which are needed to solve the problem. Construct deals with setting up the solution. Check involves solution checkup with the levels of making sense and what was learned.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(d)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Mass and weight

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

Mass is calculation of quantity of matter and weight is a measure of the force of gravitational attraction.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. The term Mass is calculation of quantity of matter and weight is a measure of the force of gravitational attraction.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(e)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Unit, kilounit, centiunit, milliunit

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

The designation associated with value is called unit. If the value is 1000 times larger than base unit it is called as ‘kilo unit’. If the value is 1/100 times as large as base unit it is denoted as ‘centi unit’. The unit is described as ‘centi unit’ when the value is 1/1000 times as large as base unit.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. The designation associated with value is called unit. If the value is 1000 times larger than base unit it is called as ‘kilo unit’. If the value is 1/100 times as large as base unit it is denoted as ‘centi unit’. The unit is described as ‘centi unit’ when the value is 1/1000 times as large as base unit.

Conclusion

Thus, the differences among given items in each of the groups is stated..

Interpretation Introduction

(f)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Significant figures, uncertain digit

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

Significant figures are the number of digits which are known accurately and the uncertain digit. Besides, the uncertain digit is a last digit written in a significant figure.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. Significant figures are the number of digits which are known accurately and the uncertain digit. Besides, the uncertain digit is a last digit written in a significant figure.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(g)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Uncertainty, exact numbers

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

The term uncertainty in an expression is denoted as plus or minus sign. Moreover, uncertainty can be expressed as significant figures. When the number is not having uncertainty, it is called exact number.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram. The term uncertainty in an expression is denoted as plus or minus sign. Moreover, uncertainty can be expressed as significant figures. When the number is not having uncertainty, it is called exact number. Besides, it is infinitely significant. Ex: a bicycle has exactly two wheels.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(h)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

The symbols = and

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

The value of equivalence between two factor is given by the symbol ‘=’ it’s value may vary with time. The symbol is referred as ‘is defined as’ or ‘is identical to’. Moreover, this relationship will never change.

Explanation of Solution

The metric system is a decimal system of the measurement based on the units for the length, meter, the mass, the kilogram.

The value of equivalence between two factor is given by the symbol ‘=’ it’s value may vary with time. 80 km = 1 hour; 50 km = 1 hr. The symbol is referred as ‘is defined as’ or ‘is identical to’. Moreover, this relationship will never change. 1 week 7 days.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(i)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Fahrenheit, Celsius, kelvin

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

Fahrenheit and Celsius scale is based on the temperature at which water freezes and boils at standard atmospheric pressure. In Fahrenheit scale the range is given as 180 degrees and in Celsius the range of temperature is division of 100 degrees. Kelvin scale is an absolute temperature scale. It’s value deals with lowest temperature of 273 ° below zero. T_K = T_°C + 273

Explanation of Solution

Fahrenheit, Celsius, kelvin are temperature scales which are common in use in United States. Fahrenheit and Celsius scale is based on the temperature at which water freezes and boils at standard atmospheric pressure. In Fahrenheit scale the range is given as 180 degrees and in Celsius the range of temperature is division of 100 degrees. Kelvin scale is an absolute temperature scale. It’s value deals with lowest temperature of 273 ° below zero. T_K = T_°C + 273

Conclusion

Thus, the differences among given items in each of the groups is stated..

Interpretation Introduction

(j)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Direct proportionality, proportionality constant

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

When one variable (x) is having a direct relationship with another variable (y), they can be expressed with the direct proportionality relationship (α). When a proportionality is denoted as an equality with a constant value, this constant value is called as proportionality constant.

Explanation of Solution

The measurement is a characteristic number of the object compared with other object. The scope of the measurement depends upon the context and event. When one variable (x) is having a direct relationship with another variable (y), they can be expressed with the direct proportionality relationship (α). i.e., x α y. When proportionality is denoted as equality with a constant value, this constant value is called as proportionality constant. x = k. y, where k is proportionality constant.

Conclusion

Thus, the differences among given items in each of the groups is stated.

Interpretation Introduction

(k)

Interpretation:

To determine the differences among items in each of the following groups is to be stated.

Density, mass, volume

Concept introduction:

The measurement is a characteristic number to the object that can be compared with other objects. The scope of the measurement depends upon the context and event. Measurement is commonly used as the international system of unit as a comparison framework. The system has 7 fundamental units like kilogram, meter, candela, ampere, kelvin and mole. The metric system is a decimal system used to measure the length, meter, the mass, the kilogram. The metric system is a single basic unit used for number of physical quantities. The quantities are derived from the SI units. For this scientific notation is most important.

Answer to Problem 113E

Density (D) of an object is given by the ratio of its mass (m) with its volume (V). In other words, the density of a substance is its mass per unit volume. The measurement deals with the quantity of matter are called as mass. The measurement of gases and liquids is carried out by volume. The value of volume can be related with density as volume = mass/density.

Explanation of Solution

The measurement is a characteristic number of the object compared with other object. The scope of the measurement depends upon the context and event. Density (D) of an object is given by the ratio of its mass (m) with its volume (V). $D =\frac{m}{V}$. The measurement deal with the quantity of matter is called as mass. The measurement of gases and liquids is carried out by volume. The value of volume can be related with density as volume = mass/density. i.e., $V =\frac{m}{D}.$

Conclusion

Thus, the differences among given items in each of the groups is stated.