Chapter
1
Chemical Arithmetic
Chemistry is basically an experimental science. In it we study Rule 5. All zeros on the right of the non zero digit are not
physical and chemical properties of substance and measure it upto significant.
possibility. The results of measurement can we reported in two steps,
Example : x 1000 has only one significant figure. Again
(a) Arithmetic number, (b) Unit of measurement.
x 378000 has three significant figures.
Every experimental measurement vary slightly from one another and
involves some error or uncertainty depending upon the skill of person Rule 6. All zeros on the right of the last non zero digit become
making the measurements and measuring instrument. The closeness of the significant, when they come from a measurement.
set of values obtained from identical measurement called precision and a Example : Suppose distance between two stations is measured to be
related term, refers to the closeness of a single measurement to its true 3050 m. It has four significant figures. The same distance can be expressed
value called accuracy.
as 3.050 km or 3.050 10 5 cm . In all these expressions, number of
Significant figures significant figures continues to be four. Thus we conclude that change in
the units of measurement of a quantity does not change the number of
In the measured value of a physical quantity, the digits about the
significant figures. By changing the position of the decimal point, the
correctness of which we are surplus the last digit which is doubtful, are
number of significant digits in the results does not change. Larger the
called the significant figures. Number of significant figures in a physical
number of significant figures obtained in a measurement, greater is the
quantity depends upon the least count of the instrument used for its
accuracy of the measurement. The reverse is also true.
measurement.
(1) Common rules for counting significant figures Following are (2) Rounding off : While rounding off measurements, we use the
some of the common rules for counting significant figures in a given following rules by convention
expression Rule 1. If the digit to be dropped is less than 5, then the preceding
Rule 1. All non zero digits are significant. digit is left unchanged.
Example : x 1234 has four significant figures. Again x 189 Example : x 7.82 is rounded off to 7.8, again x 3.94 is
has only three significant figures. rounded off to 3.9.
Rule 2. All zeros occurring between two non zero digits are Rule 2. If the digit to be dropped is more than 5, then the preceding
significant. digit is raised by one.
Example : x 1007 has four significant figures. Again Example : x = 6.87 is rounded off to 6.9, again x = 12.78 is rounded
x 1.0809 has five significant figures. off to 12.8.
Rule 3. In a number less than one, all zeros to the right of decimal Rule 3. If the digit to be dropped is 5 followed by digits other than
point and to the left of a non zero digit are not significant. zero, then the preceding digit is raised by one.
Example : x 0.0084 has only two significant digits. Again, Example : x = 16.351 is rounded off to 16.4, again x 6.758 is
x 1.0084 has five significant figures. This is on account of rule 2. rounded off to 6.8.
Rule 4. All zeros on the right of the last non zero digit in the Rule 4. If digit to be dropped is 5 or 5 followed by zeros, then preceding
decimal part are significant. digit is left unchanged, if it is even.
Example : x = 3.250 becomes 3.2 on rounding off, again
Example : x 0.00800 has three significant figures 8, 0, 0. The
zeros before 8 are not significant again 1.00 has three significant figures. x 12.650 becomes 12.6 on rounding off.
, Rule 5. If digit to be dropped is 5 or 5 followed by zeros, then the (1) C.G.S. System : Length (centimetre), Mass (gram), Time (second)
preceding digit is raised by one, if it is odd. (2) M.K.S. System : Length (metre), Mass (kilogram), Time
Example : x = 3.750 is rounded off to 3.8, again x 16.150 is (second)
rounded off to 16.2. (3) F.P.S. System : Length (foot), Mass (pound), Time
(3) Significant figure in calculation (second)
(i) Addition and subtraction : In addition and subtraction the (4) S.I. System : The 11th general conference of weights and measures
following points should be remembered (October 1960) adopted International system of units, popularly known as the SI
units. The SI has seven basic units from which all other units are derived called
(a) Every quantity should be changed into same unit.
derived units. The standard prefixes which helps to reduce the basic units are now
(b) If a quantity is expressed in the power of 10, then all the widely used.
quantities should be changed into power of 10.
(c) The result obtained after addition or subtraction, the number of Dimensional analysis : The seven basic quantities lead to a number of
figure should be equal to that of least, after decimal point. derived quantities such as pressure, volume, force, density, speed etc. The
units for such quantities can be obtained by defining the derived quantity in
(ii) Multiplication and division
terms of the base quantities using the base units. For example, speed
(a) The number of significant figures will be same if any number is
multiplied by a constant. (velocity) is expressed in distance/time. So the unit is m / s or ms 1 . The
(b) The product or division of two significant figures, will contain unit of force (mass acceleration) is kg ms 2 and the unit for
the significant figures equal to that of least.
acceleration is ms 2 .
Units for measurement
The chosen standard of measurement of a quantity which has
essentially the same nature as that of the quantity is called the unit of the
quantity. Following are the important types of system for unit,
Table 1.1 Seven basic S.I. units
Length Mass Time Temperature Electric Current Luminous Intensity Amount of
substance
metre (m) Kilogram (kg) Second (s) Kelvin (K) Ampere (A) Candela (Cd) Mole (mol)
Table 1.2 Derived Units
Physical quantity Unit Symbol
Area square metre m 2
Volume cubic metre m 3
Velocity metre per second ms –1
Acceleration metre per second square ms –2
Density kilogram per cubic metre kg m –3
Molar mass kilogram per mole kg mol –1
Molar volume cubic metre per mole m mol
3 –1
Molar concentration mole per cubic metre mol m –3
Force newton (N) kg m s –2
Pressure pascal (Pa) Nm –2
Energy work joule (J) kg m s , Nm
2 –2
Table 1.3 Standard prefixes use to reduce the basic units
Multiple Prefix Symbol Submultiple Prefix Symbol
10
24
yotta Y 10–1
deci d
1021
zetta Z 10–2
centi c
10
18
exa E 10–3
milli m
10 peta P 10 micro
15 –6
1012
tera T 10–9
nano n
1
Chemical Arithmetic
Chemistry is basically an experimental science. In it we study Rule 5. All zeros on the right of the non zero digit are not
physical and chemical properties of substance and measure it upto significant.
possibility. The results of measurement can we reported in two steps,
Example : x 1000 has only one significant figure. Again
(a) Arithmetic number, (b) Unit of measurement.
x 378000 has three significant figures.
Every experimental measurement vary slightly from one another and
involves some error or uncertainty depending upon the skill of person Rule 6. All zeros on the right of the last non zero digit become
making the measurements and measuring instrument. The closeness of the significant, when they come from a measurement.
set of values obtained from identical measurement called precision and a Example : Suppose distance between two stations is measured to be
related term, refers to the closeness of a single measurement to its true 3050 m. It has four significant figures. The same distance can be expressed
value called accuracy.
as 3.050 km or 3.050 10 5 cm . In all these expressions, number of
Significant figures significant figures continues to be four. Thus we conclude that change in
the units of measurement of a quantity does not change the number of
In the measured value of a physical quantity, the digits about the
significant figures. By changing the position of the decimal point, the
correctness of which we are surplus the last digit which is doubtful, are
number of significant digits in the results does not change. Larger the
called the significant figures. Number of significant figures in a physical
number of significant figures obtained in a measurement, greater is the
quantity depends upon the least count of the instrument used for its
accuracy of the measurement. The reverse is also true.
measurement.
(1) Common rules for counting significant figures Following are (2) Rounding off : While rounding off measurements, we use the
some of the common rules for counting significant figures in a given following rules by convention
expression Rule 1. If the digit to be dropped is less than 5, then the preceding
Rule 1. All non zero digits are significant. digit is left unchanged.
Example : x 1234 has four significant figures. Again x 189 Example : x 7.82 is rounded off to 7.8, again x 3.94 is
has only three significant figures. rounded off to 3.9.
Rule 2. All zeros occurring between two non zero digits are Rule 2. If the digit to be dropped is more than 5, then the preceding
significant. digit is raised by one.
Example : x 1007 has four significant figures. Again Example : x = 6.87 is rounded off to 6.9, again x = 12.78 is rounded
x 1.0809 has five significant figures. off to 12.8.
Rule 3. In a number less than one, all zeros to the right of decimal Rule 3. If the digit to be dropped is 5 followed by digits other than
point and to the left of a non zero digit are not significant. zero, then the preceding digit is raised by one.
Example : x 0.0084 has only two significant digits. Again, Example : x = 16.351 is rounded off to 16.4, again x 6.758 is
x 1.0084 has five significant figures. This is on account of rule 2. rounded off to 6.8.
Rule 4. All zeros on the right of the last non zero digit in the Rule 4. If digit to be dropped is 5 or 5 followed by zeros, then preceding
decimal part are significant. digit is left unchanged, if it is even.
Example : x = 3.250 becomes 3.2 on rounding off, again
Example : x 0.00800 has three significant figures 8, 0, 0. The
zeros before 8 are not significant again 1.00 has three significant figures. x 12.650 becomes 12.6 on rounding off.
, Rule 5. If digit to be dropped is 5 or 5 followed by zeros, then the (1) C.G.S. System : Length (centimetre), Mass (gram), Time (second)
preceding digit is raised by one, if it is odd. (2) M.K.S. System : Length (metre), Mass (kilogram), Time
Example : x = 3.750 is rounded off to 3.8, again x 16.150 is (second)
rounded off to 16.2. (3) F.P.S. System : Length (foot), Mass (pound), Time
(3) Significant figure in calculation (second)
(i) Addition and subtraction : In addition and subtraction the (4) S.I. System : The 11th general conference of weights and measures
following points should be remembered (October 1960) adopted International system of units, popularly known as the SI
units. The SI has seven basic units from which all other units are derived called
(a) Every quantity should be changed into same unit.
derived units. The standard prefixes which helps to reduce the basic units are now
(b) If a quantity is expressed in the power of 10, then all the widely used.
quantities should be changed into power of 10.
(c) The result obtained after addition or subtraction, the number of Dimensional analysis : The seven basic quantities lead to a number of
figure should be equal to that of least, after decimal point. derived quantities such as pressure, volume, force, density, speed etc. The
units for such quantities can be obtained by defining the derived quantity in
(ii) Multiplication and division
terms of the base quantities using the base units. For example, speed
(a) The number of significant figures will be same if any number is
multiplied by a constant. (velocity) is expressed in distance/time. So the unit is m / s or ms 1 . The
(b) The product or division of two significant figures, will contain unit of force (mass acceleration) is kg ms 2 and the unit for
the significant figures equal to that of least.
acceleration is ms 2 .
Units for measurement
The chosen standard of measurement of a quantity which has
essentially the same nature as that of the quantity is called the unit of the
quantity. Following are the important types of system for unit,
Table 1.1 Seven basic S.I. units
Length Mass Time Temperature Electric Current Luminous Intensity Amount of
substance
metre (m) Kilogram (kg) Second (s) Kelvin (K) Ampere (A) Candela (Cd) Mole (mol)
Table 1.2 Derived Units
Physical quantity Unit Symbol
Area square metre m 2
Volume cubic metre m 3
Velocity metre per second ms –1
Acceleration metre per second square ms –2
Density kilogram per cubic metre kg m –3
Molar mass kilogram per mole kg mol –1
Molar volume cubic metre per mole m mol
3 –1
Molar concentration mole per cubic metre mol m –3
Force newton (N) kg m s –2
Pressure pascal (Pa) Nm –2
Energy work joule (J) kg m s , Nm
2 –2
Table 1.3 Standard prefixes use to reduce the basic units
Multiple Prefix Symbol Submultiple Prefix Symbol
10
24
yotta Y 10–1
deci d
1021
zetta Z 10–2
centi c
10
18
exa E 10–3
milli m
10 peta P 10 micro
15 –6
1012
tera T 10–9
nano n
