Introduction for scale data definition

Introduction for scale data definition:  

                    The scale data is a ratio between the linear dimension of a representation or model and those of the object represented, as on a map or technical drawing. And scale data is a measurement. Scale Matters, develops concepts about scale. Reading scales is significant for students if they are to make use of measure devices to represent calculations using single and double number lines, to interpret locations in co-ordinate systems and to interpret many different forms of data display.

                    Scale can be identified by the concept of number line. A number line is a line inside which real numbers can be located, according to their value. In this article we shall discuss about scale data definition.

Definition and Methods of Scale Data:

Definition:

              The ratio between the linear dimension of a representation or model and those of the object represented, as on a map or technical drawing.

Methods:

             Scale factor.

             Measurement of scale.

             Proportions.

 Scale factor

              The multiplying factor for each linear measurement of an object when it is to be enlarged about a given centre of enlargement. A scale factor can be positive, negative or fractional. If the scale factor is positive, the image is larger than the object and on the same side of centre of enlargement as the object as the object. If the scale factor is fractional positive, the image will be smaller than the object,  but on the same side of the centre of enlargement. If the scale factor is negative, the image will be on the opposite side of the centre of enlargement and will be invented.

              For example, doubling distance corresponds to a scale factor of 2 for distance, while cutting a cake in half results in pieces with a scale factor of ½.

Measurement of scale:

               We do measurements in our routine life in a number of conditions. For example, we calculate the length of a cloth for stitching, the area of a wall for white washing, the perimeter of a land for fencing and the volume of a container for filling. Based upon the measurements, we do further calculations according to our needs. The branch of mathematics which deals with the measure of lengths, angles, areas, perimeters and volumes of plane.

Area and Perimeter:

              Rectangle:

                          Area = l × b sq.units

                          Perimeter = 2 (l + b) units

                         d = `sqrt((l^2)+(b^2))` units

            Parallelogram:

                           Area = b × h sq.units

                          Perimeter = 2(a + b) units.

           Triangle with a given base and height:

                         Area = `1 / 2` (b × h) sq.units

           Quadrilateral:

                        Area = 21 d × (h1 + h2) Sq.units

Proportion for Scale Data Definition:

            A relation giving the equality of two ratios, in the form

                                         `a / b` = `c / d`

            Before it was written as a: b :: c: d, which has become obsolete these days. Here a and b are recognized as extremes, b and c are known as means. If two ratios are in proportion then the product of extremes must be equal to the product of means. ad = bc.

Example 1:
            Jane ran 150 meters in 20 seconds. How long did she take to run 1 meter?

Solution:

Step 1: Think of the word problem as:

              If, 150 then 20, If 1 then, how many?

Step 2: Write the proportional relationship:

             150 ? 20

             1? (1 / 150) x 20 = 0.15

Answer: She took 0.133 seconds

Example 2:

A car travels 150 miles in 4 hours. How far would it travel in 6 hours?

Solution:

Step 1: Think of the word problem as:

              If 4 then 150. If 6 then how many?

Step 2: Write the proportional relationship:

                 4 ? 150

                 6 ? `(6 / 4)` x 150 = 225

Answer: He traveled 225 miles.