What is the scale in 1 cm 10 meters. Map scale. Fig.53. Normal transverse scale

Scale(German Maßstab, lit. "measuring stick": Mass"measure", Stab"stick") - in the general case, the ratio of two linear dimensions. In many areas of practical application, scale is the ratio of the size of an image to the size of the depicted object.

The concept is most common in geodesy, cartography and design - the ratio of the size of the image of an object to its natural size. A person is not able to depict large objects, such as a house, in full size, therefore, when depicting a large object in a drawing, drawing or layout, the size of the object is reduced several times: two, five, ten, one hundred, one thousand, and so on. The number showing how many times the depicted object is reduced is the scale. The scale is also used when depicting the microworld. A person cannot depict a living cell, which he examines under a microscope, in full size and therefore increases the size of its image by several thousand times. The number showing how many times the real phenomenon is enlarged or reduced when it is depicted is defined as a scale.

Scale in geodesy, cartography and engineering

Scale shows how many times each line drawn on a map or drawing is less or more than its actual size. There are three types of scale: numerical, named, graphic.

Scales on maps and plans can be represented numerically or graphically.

Numerical scale is written as a fraction, the numerator of which is one, and the denominator is the degree of reduction of the projection. For example, a scale of 1:5000 shows that 1 cm on the plan corresponds to 5000 cm (50 m) on the ground.

Larger is the scale with the smaller denominator. For example, a scale of 1: 1,000 is larger than a scale of 1: 25,000. In other words, with more large scale the object is depicted larger (bigger), with more small scale- the same object is depicted smaller (smaller).

Named Scale shows what distance on the ground corresponds to 1 cm on the plan. It is written, for example: “There are 100 kilometers in 1 centimeter”, or “1 cm = 100 km”.

Graphic scales subdivided into linear and transverse.

• Linear scale- this is a graphical scale in the form of a scale bar, divided into equal parts.
• Cross scale- this is a graphical scale in the form of a nomogram, the construction of which is based on the proportionality of segments of parallel lines intersecting the sides of the angle. The transverse scale is used for more accurate measurements of the lengths of lines on the plans. The transverse scale is used as follows: they postpone the length measurement on the bottom line of the transverse scale so that one end (right) is at the whole division of OM, and the left one goes beyond 0. If the left leg falls between the tenth divisions of the left segment (from 0), then raise both legs of the meter up until the left leg hits the intersection of a transvensal and some horizontal line. In this case, the right leg of the meter should be on the same horizontal line. The smallest CD = 0.2 mm, and the accuracy is 0.1.

Scale Accuracy- this is a segment of the horizontal line, corresponding to 0.1 mm on the plan. The value of 0.1 mm for determining the accuracy of the scale is adopted due to the fact that this is the minimum segment that a person can distinguish with the naked eye. For example, for a scale of 1:10,000, the scale accuracy will be 1 m. In this scale, 1 cm on the plan corresponds to 10,000 cm (100 m) on the ground, 1 mm - 1,000 cm (10 m), 0.1 mm - 100 cm (1 m).

The scales of images in the drawings should be selected from the following range:

When designing master plans for large objects, it is allowed to use scales of 1:2,000; 1:5000; 1:10,000; 1:20,000; 1:25,000; 1:50,000.
In necessary cases, it is allowed to use magnification scales (100n):1, where n is an integer.

Scale in photography

When photographing, scale is understood as the ratio of the linear size of the image obtained on a photographic film or photosensitive matrix to the linear size of the projection of the corresponding part of the scene onto a plane perpendicular to the direction to the camera.

Some photographers measure scale as the ratio of the size of an object to the size of its image on paper, screen, or other media. The correct scaling technique depends on the context in which the image is used.

Scale is important in calculating the depth of field. A very wide range of scales is available to photographers - from almost infinitely small (for example, when shooting celestial bodies) to very large (without the use of special optics, it is possible to obtain scales of the order of 10:1).

Macro photography is traditionally understood as shooting at a scale of 1: 1 or larger. However, with the widespread use of compact digital cameras, this term has also been used to refer to shooting close to the lens (usually closer than 50 cm) small objects. This is due to the necessary change in the mode of operation of the autofocus system in such conditions, however, from the point of view of the classical definition of macro photography, such an interpretation is incorrect.

Scale in modeling

For each type of scale (bench) modeling, scale series are defined, consisting of several scales of varying degrees of reduction, and for different types of modeling (aircraft modeling, ship modeling, railway, automotive, military equipment), their own, historically established, scale series are defined, which usually do not intersect .

The scale in modeling is calculated by the formula:

Where: L - original parameter, M - required scale, X - desired value

For example:

With a scale of 1/72, and an original parameter of 7500 mm, the solution will look like;

7500 mm / 72 = 104.1 mm.

The resulting value is 104.1 mm, there is the desired value at a scale of 1/72.

time scale

In programming

In time-sharing operating systems, it is extremely important to provide individual tasks with the so-called "real time mode", in which the processing of external events is ensured without additional delays and gaps. The term “real time scale” is also used for this, however, this is a terminological convention that has nothing to do with the original meaning of the word “scale”.

In film technology

Time scale - a quantitative measure of slowing down or speeding up movement, equal to the ratio of the projected frame rate to the filming frame rate. So, if the projection frame rate is 24 frames per second, and the filming was done at 72 frames per second, the time scale is 1:3. The 2:1 time scale means twice the speed of the process on the screen compared to the usual one.

In mathematics

Scale is the ratio of two linear dimensions. In many areas of practical application, scale is the ratio of the size of an image to the size of the depicted object. In mathematics, the scale is defined as the ratio of the distance on the map to the corresponding distance in the real area. A scale of 1:100,000 means that 1 cm on the map corresponds to 100,000 cm = 1,000 m = 1 km on the ground.

/ WHAT IS SCALE

Scale. Scale types

Geography. 7th grade

What is scale?

The scale shows how many times the distance on the map is less than the corresponding distance on the ground.

A scale of 1:10,000 (read one ten-thousandth) shows that each centimeter on the map corresponds to 10,000 centimeters on the ground.

What does scale mean

Scale types

What kind of scale is shown here? Which one is missing?

Write in 1 cm -

Since there are 100 centimeters in 1 meter, you need to remove two zeros

Since there are 1000 meters in 1 kilometer, you need to remove three more zeros (if possible)

Write the remaining number after the dash, indicate meters or kilometers

How to convert a numerical scale to a named one

Scale conversion from numerical to named

Check answers

in 1 cm - 5 m

in 1 cm - 15 m

in 1 cm - 500 m

in 1 cm - 2 km

in 1 cm - 30 km

in 1 cm - 600 km

in 1 cm - 15 km

Exercises. Convert scale from numerical to named

How to calculate scale 1:50?

The scale is used to place in the drawing an area that is actually many times larger. At a scale of 1:50, all dimensions are taken 50 times smaller than in reality. For example, the drawing is drawn on a scale of 1:50. On it, the size of 50 meters is taken as 1 meter. If you want to depict a shop 5 meters long, then in the figure its length will be 10 cm. Such a small scale is used in construction drawings for a graphic representation of a small area (landscape design). Conclusion: when drawing with a scale of 1:50, all initial dimensions must be divided by 50.

Mirra mi

A scale of 1 to 50 means that in the drawing all objects, lines are reduced by 50 times what they actually are. That is, 1 cm in the drawing is 50 cm in reality. Therefore, while reading such a drawing, each centimeter must be multiplied by 50:

1 cm is 50 cm,

2 cm is 100 cm,

10 cm is 500 cm, etc.

A scale of 1:50 means that the object (drawing, map, graph, drawing, object, sketch, etc.) that we see is reduced fifty times compared to the original size. Where the length is shown, for example, one centimeter in the original means fifty centimeters.

Zolotynka

To understand what a 1:50 scale is, consider an example: suppose we have a model car produced in 1:50 scale. This means that the real car is 50 times larger than our model.

The same applies to maps: when we draw a locality to scale on a sheet of paper or a computer screen, we reduce the distances by 50 times, but be sure to preserve all the features of the terrain and all proportions. The scale clearly shows the relationship between distances on the map and distances on the ground. This makes the map convenient for us, as we get visual information that can be used to easily calculate ground distances.

Those. in order to create a model on a scale of 1 to 50 (anything - an object, terrain), you need to divide the real size by 50.

Azamatik

To do this, let's use an example.

A scale of 1 to 50 means, for example, that 50 kilometers is taken as 1 kilometer; 50 meters is taken as 1 meter; 50 centimeters as 1 centimeter and so on.

Let's take a real football field, which is 100 meters long and 50 meters wide.

To depict this field on a piece of paper on a scale of 1 to 50, we divide both the width and the length by 50 (50 m).

Therefore, this football field on a scale of 1:50 will be 2 meters long and 1 meter wide.

Moreljuba

Scale is a very necessary and important thing. It is very important when creating drawings of the area and maps. If we are talking about a scale of 1:50, then this means that all real objects, when transferred to our drawing, must be reduced in size by 50 times. In other words, the dimensions of the objects should be divided by 50. For example, if we need to put an object 100 centimeters long on the drawing, we reduce it to 2 centimeters (100/50).

Quite simply, if this is some kind of drawing, then this means that all the details, say, a model of a ship, are reduced by 50 times and in order to represent the true size of the ship from which this drawing was made, you will need to increase the model by 50 times, that is, multiply the size all parts for 50.

Razyusha

If you need to make rooms, some kind of object on a scale of 1:50, then you need to do it this way: divide each length by 50 cm, draw the result on paper. Let's say a wall 6 m long in the drawing will be 12 cm long. How is this calculated:

6 m = 600 cm,

600: 50 = 12 cm.

Pollack tail

It turns out that all objects in the figure are reduced by fifty times. In order to calculate the scale of the object, it is necessary to measure the picture with a regular ruler after 1 cm, multiply by 50. Actually, this will turn out to be the real scale of the object.

The question is on the verge of fantasy. The scale of one to fifty is the ratio of one scale unit containing 50 real scale units. For example, 1 cm of the established scale contains 50 cm of the real one.

What is scale?

Daria Remizova

Scale
(German Maßstab, from Maß - measure, size and Stab - stick), the ratio of the length of segments in a drawing, plan, aerial photograph or map to the lengths of their corresponding segments in kind. The numerical Scale defined in this way is an abstract number, greater than 1 in the cases of drawings of small parts of machines and devices, as well as many micro-objects, and less than 1 in other cases, when the denominator of the fraction (with the numerator equal to 1) shows the degree of reduction in the size of the image of objects relative to their actual sizes. The scale of plans and topographic maps is a constant value; The scale of geographical maps is a variable value. For practice, a linear scale is important, that is, a straight line divided into equal segments with captions indicating the lengths of the segments corresponding to them in kind. For more accurate drawing and measurement of lines on plans, a so-called transverse scale is built. The transverse scale is a linear scale parallel to which a series of equally spaced horizontal lines crossed by perpendiculars (verticals) and oblique lines (transverses) is drawn. The principle of construction and use of the transverse scale. is clear from the figure given for a numerical scale of 1: 5000. The segment of the transverse scale, marked in the figure with dots, corresponds on the ground to the line 200 + 60 + 6 = 266 m. A metal ruler is also called a transverse scale, on which an image of such a pattern is carved with very thin lines , sometimes without any inscriptions. This makes it easy to use it in the case of any numerical scale used in practice.
Scale 1:200 means that 1 unit of measurement in the figure or drawing corresponds to 200 units of measurement in space. For example: a topographic map - atlas of the Tver region has a scale of 1:200000. This means that 1 centimeter on the map is equal to 2 kilometers on the ground.

Dmitry Mosendz

Scale 1:200 means that 1 unit of measurement in the figure or drawing corresponds to 200 units of measurement in space. For example: a topographic map - atlas of the Tver region has a scale of 1:200000. This means that 1 centimeter on the map is equal to 2 kilometers on the ground.

The scale is the degree to which lines are reduced when they are transferred to a plan or map.

The numerical scale is a proper fraction, the numerator of which is one, and the denominator is the number (M), showing the degree of reduction of the lines.

For example, a numerical scale or 1:2000 shows that all lines on the ground are reduced by M = 2000 times, or 1 cm on a plan or map corresponds to 2000 cm in reality, or 20 m is contained in one centimeter.

A linear scale is a graph used to determine the distances between points on a map or plan.

The construction of a linear scale includes drawing a straight line on paper, dividing it into equal segments of 2 or 1 cm, and dividing the first segment into smaller divisions, for example, 2 or 1 mm each (Fig. 52).

Rice. 52. Linear scale

On fig. 52 shows that one centimeter on a 1:10000 scale map is 100 m on the ground. Two centimeters will contain 200 m. A two-centimeter segment is divided into 20 parts, therefore, 1 mm on the map will correspond to 10 m on the ground. The plotted distance on a linear scale is 590 m.

The transverse scale is a graph by which distances are determined on a plan or map with an accepted accuracy of 0.2 mm. Such a graph is shown in Fig. 53.

Fig.53. Normal transverse scale

On this graph, the segment ab is the smallest division of the transverse scale. The base A of the transverse scale is 2 cm and can be divided into m equal parts. The height H of this scale is 2.5 cm and generally includes n equal parts.

Segment , and segment .

From the ratio we get .

For normal transverse scale m = n=10, then

ab= 0.2 mm.

Cross Scale Accuracy t- this is the distance on the ground, corresponding to the accuracy of graphic constructions of 0.2 mm:

where M is the denominator of the numerical scale.

For example, the accuracy of the transverse scale 1:25000 will be

or t = 5 m.

Example1. Determine the length of the measured distance se in scales 1:5000 and 1:25000.

On a scale of 1:5000, 2 cm is actually 100 m, and on a scale of 1:25,000 it is 500 m. Since the base of the scale is divided into 10 equal parts, one tenth of it (the segment cd) corresponds to a distance of 10 m on a scale of 1:5000, and on a scale of 1:25000 - 50 m. The height of the scale H is divided into 10 equal parts, therefore, in the segment ab contains 1 m when using a scale of 1:5000 and 5 m when using a scale of 1:25000.

In order to measure the distances between points on the map, it is necessary to touch the points with the compass needles and apply the resulting solution of the compass to the transverse scale so that one needle is at the intersection of the inclined and horizontal scale lines (point s), and the other - on the horizontal and vertical lines (point e). Measured segment se consists of three parts so, or and re. These parts correspond to distances on the ground on a scale of 1:5000 40 + 6 + 4 = 446 m, and on a scale of 1:25000 - 200 + 30 + 2000 = 2230 m.

Example 2. Determine on the map of scale 1:25000 the distance between the point in the square 6507 "Elevation 214.3" and the point in the square 6508 "Elevation 197.1" (see Fig. 2).

As a result of the measurement on a real map, and not on its schematic representation, the result was obtained: 1480 m.

Scale 1: 100,000

1 mm on the map - 100 m (0.1 km) on the ground

1 cm on the map - 1000 m (1 km) on the ground

10 cm on the map - 10000 m (10 km) on the ground

Scale 1:10000

1 mm on the map - 10 m (0.01 km) on the ground

1 cm on the map - 100 m (0.1 km) on the ground

10 cm on the map - 1000m (1 km) on the ground

Scale 1:5000

1 mm on the map - 5 m (0.005 km) on the ground

1 cm on the map - 50 m (0.05 km) on the ground

10 cm on the map - 500 m (0.5 km) on the ground

Scale 1:2000

1 mm on the map - 2 m (0.002 km) on the ground

1 cm on the map - 20 m (0.02 km) on the ground

10 cm on the map - 200 m (0.2 km) on the ground

Scale 1:1000

1 mm on the map - 100 cm (1 m) on the ground

1 cm on the map - 1000cm (10 m) on the ground

10 cm on the map - 100 m on the ground

Scale 1:500

1 mm on the map - 50 cm (0.5 meters) on the ground

1 cm on the map - 5 m on the ground

10 cm on the map - 50 m on the ground

Scale 1:200

1 mm on the map - 0.2 m (20 cm) on the ground

1 cm on the map - 2 m (200 cm) on the ground

10 cm on the map - 20 m (0.2 km) on the ground

Scale 1:100

1 mm on the map - 0.1 m (10 cm) on the ground

1 cm on the map - 1 m (100 cm) on the ground

10 cm on the map - 10m (0.01 km) on the ground

Convert the map's numerical scale to a named one:

Solution:

To make it easier to translate a numerical scale into a named one, you need to calculate how many zeros the number in the denominator ends with.

For example, on a scale of 1:500,000, there are five zeros in the denominator after the number 5.

If after the number in the denominator there are five or more zeros, then by closing (with a finger, a pen or simply crossing out) five zeros, we get the number of kilometers on the ground corresponding to 1 centimeter on the map.

Example for scale 1: 500,000

There are five zeros in the denominator after the number. Closing them, we get for the named scale: 1 cm on the map 5 kilometers on the ground.

If after the number in the denominator there are less than five zeros, then by closing two zeros, we get the number of meters on the ground corresponding to 1 centimeter on the map.

If, for example, in the denominator of the scale 1: 10,000 we close two zeros, we get:

in 1 cm - 100 m.

Answers:

in 1 cm - 2 km;

in 1 cm - 100 km;

in 1 cm - 250 m.

Use a ruler, overlay on maps to make it easier to measure distances.

Convert a named scale to a numerical one:

in 1 cm - 500 m

in 1 cm - 10 km

in 1 cm - 250 km

Solution:

For easier translation of a named scale into a numerical scale, you need to convert the distance on the ground indicated in the named scale to centimeters.

If the distance on the ground is expressed in meters, then to get the denominator of the numerical scale, you need to assign two zeros, if in kilometers, then five zeros.

For example, for a named scale of 1 cm - 100 m, the distance on the ground is expressed in meters, so for a numerical scale we assign two zeros and get: 1: 10,000.

For a scale of 1 cm - 5 km, we assign five zeros to the five and get: 1: 500,000.

Answers:

Maps, depending on the scale, are conventionally divided into the following types:

topographic plans - 1:400 - 1:5,000;

large-scale topographic maps - 1:10,000 - 1:100,000;

medium-scale topographic maps - from 1:200,000 - 1:1,000,000;

small-scale topographic maps - less than 1:1,000,000.

Scale maps:

1:10,000 (1cm=100m)

1:25,000 (1cm=100m)

1:50,000 (1cm=500m)

1:100,000 (1cm=1000m)

called large scale.

Tale about the map in scale 1:1

Once upon a time there was a Capricious King. One day he traveled around his kingdom and saw how great and beautiful his land was. He saw winding rivers, huge lakes, high mountains and wonderful cities. He became proud of his possessions and wanted the whole world to know about them. And so, the Capricious King ordered the cartographers to create a map of the kingdom. The cartographers worked for a whole year and finally presented the King with a wonderful map, on which all the mountain ranges, large cities and large lakes and rivers were indicated.

However, the Capricious King was not satisfied. He wanted to see on the map not only the outlines of the mountain ranges, but also the image of each mountain peak. Not only large cities, but also small ones and villages. He wanted to see small rivers flowing into rivers.

The cartographers set to work again, worked for many years and drew another map, twice the size of the previous one. But now the King wished that the map showed passes between mountain peaks, small lakes in the forests, streams, peasant houses on the outskirts of villages. Cartographers drew more and more new maps.

The capricious King died without waiting for the end of the work. Successors one by one came to the throne and died in turn, and the map was drawn up and drawn up. Each king hired new cartographers to map the kingdom, but each time he remained dissatisfied with the fruits of labor, finding the map insufficiently detailed.

Finally the cartographers drew an Incredible map!!! The map depicted the entire kingdom in great detail - and was exactly the same size as the kingdom itself. Now no one could tell the difference between the map and the kingdom.

Where were the Capricious Kings going to store their wonderful map? The casket for such a card is not enough. You will need a huge room like a hangar, and in it the map will lie in many layers. Do you really need such a card? After all, a life-size map can be successfully replaced by the terrain itself ..))))

What is scale? Scale - in the general case, the ratio of two linear dimensions. In areas of practical application, the scale is the ratio of the size of the image to the size of the depicted object.

That is, on maps, plans, aerial or satellite images, this is the ratio of the length of the segment to its actual length on the ground. It is accepted, on maps, to take 1 centimeter as a unit of measurement, and on the ground to measure the distance in meters.

Types of indication of scales

There are three types of scaling:

• numerical;
• named;
• linear.

Numerical scale(the most common and convenient) - a fractional scale, where the numerator is one, and the denominator is a number showing how many times the given image of the territory is reduced (example: 1:100,000; 1:15,000). Both figures are indicated in centimeters, which makes it impossible to make a mistake in translation, converting one unit of measurement to another. But in practice, the use of such a scale is not convenient. Therefore, when working directly on the ground, the numerical scale is most often translated into a named one.

Named (or verbal) scale- a verbal indication of what distance on the ground corresponds to 1 centimeter on the map (example: 1 cm 5 km or 1 cm = 500 meters). This kind of scale is understandable to the human mind, but it will be difficult to make calculations and very easy to make a mistake.

There is also a third type of scale indication. This is a linear scale.

Linear scale- an auxiliary measuring ruler on the maps for quick measurement of distances, without calculations.

The scale of the maps is always the same at all its points.

Standard scales

In Russia, standard numerical scales are adopted:

1:1 000 000
1:500 000
1:200 000
1:100 000
1:50 000
1:25 000
1:10 000.

*For special purposes, topographic maps are also created at scales of 1:5,000 and 1:2,000.

Converting a numerical scale to a named one

Since the lengths of lines on the ground are usually measured in meters, and on maps and plans - in centimeters, it is most convenient to express the scales in verbal form, for example:

There are 100 meters in one centimeter. This corresponds to a numerical scale of 1:10,000. Since 1 meter equals 100 centimeters, the number of meters on the ground contained in 1 cm on the map is easily determined by dividing the denominator of the numerical scale by 100. Or by 100,000 to convert to km.

That is, a numerical scale of 1:30,000 means that there are 300 meters (30,000/100) in 1 cm on the map.

Each card has scale- a number that shows how many centimeters on the ground correspond to one centimeter on the map.

map scale usually listed on it. Record 1: 100,000,000 means that if the distance between two points on the map is 1 cm, then the distance between the corresponding points on its terrain is 100,000,000 cm.

May be listed in numerical form as a fraction– numerical scale (for example, 1: 200,000). And it can be marked in linear form: as a simple line or strip divided into units of length (usually kilometers or miles).

The larger the scale of the map, the more detailed the elements of its content can be depicted on it, and vice versa, the smaller the scale, the more extensive space can be shown on the map sheet, but the terrain on it is depicted with less detail.

Scale is a fraction whose numerator is one. To determine which of the scales is larger and by how many times, let's recall the rule for comparing fractions with the same numerators: of two fractions with the same numerators, the one with the smaller denominator is larger.

The ratio of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the scale of the map.

How does this knowledge help us in solving problems in mathematics?

Example 1

Let's look at two cards. A distance of 900 km between points A and B corresponds on one map to a distance of 3 cm. A distance of 1,500 km between points C and D corresponds to a distance of 5 cm on another map. Let us prove that the scales of the maps are the same.

Solution.

Find the scale of each map.

900 km = 90,000,000 cm;

the scale of the first map is: 3: 90,000,000 = 1: 30,000,000.

1500 km = 150,000,000 cm;

the scale of the second map is: 5: 150,000,000 = 1: 30,000,000.

Answer. The scales of the maps are the same, i.e. are equal to 1:30,000,000.

Example 2

The scale of the map is 1: 1,000,000. Let's find the distance between points A and B on the ground, if on the map
AB = 3.42 cm?

Solution.

Let's make an equation: the ratio of AB \u003d 3.42 cm on the map to the unknown distance x (in centimeters) is equal to the ratio between the same points A and B on the ground to the map scale:

3.42: x = 1: 1,000,000;

x 1 \u003d 3.42 1,000,000;

x \u003d 3,420,000 cm \u003d 34.2 km.

Answer: the distance between points A and B on the ground is 34.2 km.

Example 3

The scale of the map is 1: 1,000,000. The distance between points on the ground is 38.4 km. What is the distance between these points on the map?

Solution.

The ratio of the unknown distance x between points A and B on the map to the distance in centimeters between the same points A and B on the ground is equal to the scale of the map.

38.4 km = 3,840,000 cm;

x: 3,840,000 = 1: 1,000,000;

x \u003d 3,840,000 1: 1,000,000 \u003d 3.84.

Answer: the distance between points A and B on the map is 3.84 cm.

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