Unit conversion chart

Introduction: Units may be written in full or using the agreed symbols, but no other abbreviation may be used. The letter ‘s’ is never added to symbols to indicate the plural form. A full stop is not written after symbols for units unless it occurs at the end of a sentence. When unit symbols are combined as a quotient

e.g. metre per second, it is recommended that they may be written as m/s or better still as ms^-1. Three decimal signs are used commonly internationally and they are the full point, followed by the mid-point and lastly the comma. The full point sometimes is used as a sign of multiplication and the comma for spacing the digits in large numbers; we shall be on the safe side if we use the mid-point for decimals.

Basic units of measurement: the unit of measure for length is metre and it is denoted by the letter ‘m’. The unit of measure for mass is kilogram and it is denoted by the symbol ‘kg’. The unit of measure for time is second and it is denoted by the symbol‘s’.

Unit conversion chart: 
1. Units of weight: SI unit for weight is kg and let us understand unit weight through weight conversions  chart. Following are the units of weight and weight  conversions chart
(i) 10 milligrams = 1 centigram 10 mg = 1 cg
(ii) 100 centigram = 1 gram 100 cg = 1 g
(iii) 100 grams = 1 kilogram 1000 g = 1 kg
(iv) 100 kilograms = 1 quintal
(v) 10 quintals = 1 metric tonne
2. Units for volume: The SI unit of volume is cubic metres (m^3). Litre is also sometimes used as the unit of volume. Following are the units of volume and volume conversions:
(i) 1 cm^3 = 1 ml = 1 cm × 1 cm × 1 cm = 10 mm × 10 mm × 10 mm = 1000 mm^3
(ii) 1 litre = 1000 ml = 1000 cm^3
(iii) 1 m^3 = 1 m × 1 m × 1 m = 100 cm × 100 cm × 100 cm = 10^6 cm^3 = 1000 litre = 1 kilolitre
(iv) 1 dm^3 = 1000 cm^3
(v) 1 m^3 = 1000 dm^3
(vi) 1 km^3 = 10^9 m^3
3. Units of length: The SI unit of length is metre.Following are the unit of length and length conversions:
(i) 10 millimetres = 1 centimetre 10 mm = 1 cm
(ii) 100 centimetres = 1 metres 100 cm = 1 m
(iii) 1000 metres = 1 kilometre 1000 m = 1 km
4. Square and cubic units
1 cm^2 = 100 mm^2 1 cm^3 = 1000 mm^3
1 m^2 = 10000 cm^2 1 m^3 = 1000000 cm^3
1 litre = 1000 cm^3
1 m^3 = 1000 litres
1 hectare = 10000 m^2.

Introduction to vectors

Introduction to vectors: In mathematics we have many systems which are employed to handle problems in Geometry, Mechanics and other branches of Applied Mathematics. Vectors constitute one of these systems. Vectors facilitate analytic study of the previous type of physical objects which have direction in addition to magnitude. No doubt, the set of real numbers provides an analytical tool for study of various types of physical problems for which vectors are useful.

The use of vectors in these problems is more natural. We have to associate a physical entity involving direction to the set of real numbers for we have to split up the entity into components and associate a number with each. The use of vectors avoids this splitting up. What is a vector? Quantities that have magnitude as well as direction are called vectors.

Definition of a vector: A directed line segment is called a vector. A vector from P to Q is denoted by  . P and Q are called respectively initial and terminal points of the vector  . Vector Example: Such quantities are called vectors Displacement, velocity, acceleration, momentum, weight, force etc.

Types of vectors are Zero or null vector: A vector whose initial and terminal points are coincident is called the zero or the null vector. Vectors other than the null vector are called proper vectors.

Unit vector: A vector whose modulus is unity is called the unit vector.

Like and unlike vectors: Vectors are said to be like when they have the same sense of direction and unlike when they have opposite directions.

Collinear or parallel vectors: Vectors having the same or parallel supports are called collinear vectors.

Co-initial vectors: Vectors having the same initial point are called co-initial vectors.

Scalars quantities: Quantities that have only magnitude but no direction are called scalars. For example, time, mass, volume, population, temperature, energy, power are all scalars. We need a unit and a real number to specify a scalar. For example, 3 hours,  2.5 kg, 8 cubic centimetres, 23°F etc.

Vector and scalar quantities

Physical quantities are divided into two categories- Vector and scalar. Those quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or scalars. Example of scalars are mass, volume, density, work, temperature etc. Second kinds of quantities are those which have both magnitude and direction.


Co-planar vectors: A system of vectors is said to be coplanar, if their supports are parallel to the same plane. Two vectors are always coplanar.

Percentile (Statistics)

Define percentile:

Instead of dividing the total frequency into 4 parts by quartiles, we may divide it into 100 parts by what are called percentiles. Or we may divide into 10 parts by decile. The theory of percentiles is precisely analogous to that of the quartiles. Like the quartiles, there may, for instance, be certain indeterminacies in their exact percentile definition which are removed by supplementary conventions. Percentiles can be obtained by arithmetical or graphical interpolation. Percentiles have obvious meanings.

These quantities such as quartiles, deciles and percentiles, which divide the total frequency into a number of parts, are called quantiles or grades, and when we speak of the grade of an individual we mean thereby the proportion of the total frequency which lies below it. For example, when we say that a student has scored 75 percentile, we mean that of the total number of students who have appeared for the test, 75% of them have scored below this student.

Finding the percentile:

The percentile can be conveniently found by a graphical method which is an extension  of the graphical method of finding the median. Against the variate value as abscissa we graph as ordinate the cumulated frequency up to and including the corresponding variate value. This is called the distribution curve. By reading off the ordinate corresponding to a given variate we can find the number of members of the population bearing that or lower value. Similarly, by reading off the variate corresponding to the given ordinate we can find the percentiles.

A somewhat similar form of graph (with the percentiles as abscissa and the variate a ordinate) was formerly in use and was known as Galton’s ogive. The curve was not, however, always shaped like an ogive. The distribution curve appears to provide a more natural method of representation and a better name. We recognize it as the graph of the integral of the frequency curve.

Percentile uses:

In statistics percentile has been found to be very useful when dealing with non measurable characters. For example, the capacity of different boys in a class as regards some school subject cannot be directly measured, but it may not be very difficult for the teacher to arrange them in order of merit as regards this particular character. If the boys are then numbered up in that order, the number of each boy, or his rank, becomes more or less his representative of his percentile. So the third ranker in a group of 50 boys would be the 94th percentile and so on.