Unit segment A segment whose length is taken as a unit of length is called a unit segment. Which segment is called a unit segment? What is a unit segment

Natural numbers can be depicted on a ray. Let's construct a ray with the beginning at point O, directing it from left to right, marking the direction with an arrow.

Let us assign the number 0 (zero) to the beginning of the ray (point O). Let us lay off a segment OA of arbitrary length from point O. Let us associate point A with the number 1 (one). The length of the segment OA will be considered equal to 1 (unit). The segment AB = 1 is called single segment. Let us lay off the segment AB = OA from point A in the direction of the ray. Let us assign the number 2 to point B. Note that point B is located from point O at a distance twice as great as point A. This means that the length of the segment OB is equal to 2 (two units). Continuing to plot segments equal to one in the direction of the ray, we will obtain points that correspond to the numbers 3, 4, 5, etc. These points are removed from point O by 3, 4, 5, etc., respectively. units.

A beam constructed in this way is called coordinate or numerical. The beginning of the number line, point O, is called starting point. The numbers assigned to points on this ray are called coordinates these points (hence: coordinate ray). They write: O(0), A(1), B(2), read: “ point O with coordinate 0 (zero), point A with coordinate 1 (one), point B with coordinate 2 (two)" etc.

Any natural number n can be depicted on a coordinate ray, and the corresponding point P will be removed from point O by n units. They write: OP = n and P( n) - point P (read: "pe") with coordinate n(read: "en"). For example, to mark point K(107) on a number line, it is necessary to plot 107 segments equal to one from point O. You can select a segment of any length as a single segment. Often the length of a unit segment is chosen such that it is possible to depict the necessary natural numbers on a number line within the limits of the picture. Consider an example

5.2. Scale

An important application of the number beam is in scales and charts. They are used in measuring instruments and devices with which various quantities are measured. One of the main elements of measuring instruments is the scale. It is a numerical beam applied to a metal, wood, plastic, glass or other base. Often the scale is made in the form of a circle or part of a circle, which are divided by strokes into equal parts (divisions-arcs) like a number line. Each stroke on a straight or circular scale is assigned a specific number. This is the value of the measured quantity. For example, the number 0 on the thermometer scale corresponds to a temperature of 0 0 C, read: “ zero degrees Celsius" This is the temperature at which ice begins to melt (or water begins to freeze).

Using measuring instruments and instruments with scales, determine the value of the measured quantity by position pointer on the scale. Most often, arrows serve as indicators. They can move along the scale, marking the value of the measured value (for example, a clock hand, a scale hand, a speedometer hand - a device for measuring speed, Figure 3.1.). The boundary of a column of mercury or tinted alcohol in a thermometer is similar to a moving arrow (Figure 3.1). In some instruments, it is not the arrow that moves along the scale, but the scale that moves relative to the stationary arrow (mark, line), for example, in floor scales. In some instruments (ruler, tape measure), the pointer is the boundaries of the object being measured.

The spaces (parts of the scale) between adjacent scale strokes are called divisions. The distance between adjacent strokes, expressed in units of the measured value, is called the division price(the difference in numbers that correspond to adjacent scale strokes.) For example, the price of the speedometer division in Figure 3.1. is equal to 20 km/h (twenty kilometers per hour), and the division price of the room thermometer in Figure 3.1. equal to 1 0 C (one degree Celsius).

Diagram

To visually display quantities, line, column or pie charts are used. The diagram consists of a numerical ray-scale directed from left to right or from bottom to top. In addition, the diagram contains segments or rectangles (columns) depicting the compared values. In this case, the length of segments or columns in scale units is equal to the corresponding values. On the diagram, near the numerical ray-scale, sign the name of the units of measurement in which the quantities are plotted. In Figure 3.2. shows a bar chart, and Figure 3.3 shows a line chart.

3.2.1. Quantities and instruments for measuring them

The table shows the names of some quantities, as well as devices and instruments designed to measure them. (Bold type indicates the basic units of the International System of Units.)

5.2.2. Thermometers. Temperature measurement

Figure 3.4 shows thermometers that use different temperature scales: Reaumur (°R), Celsius (°C) and Fahrenheit (°F). They use the same temperature range - the difference between the boiling temperatures of water and the melting temperatures of ice. This interval is divided into a different number of parts: in the Reaumur scale - into 80 parts, in the Celsius scale - into 100 parts, in the Fahrenheit scale - into 180 parts. Moreover, in the Reaumur and Celsius scales, the temperature of ice melting corresponds to the number 0 (zero), and in the Fahrenheit scale - to the number 32. The temperature units in these thermometers are: degree Reaumur, degree Celsius, degree Fahrenheit. Thermometers use the property of liquids (alcohol, mercury) to expand when heated. At the same time, different liquids expand differently when heated, as can be seen in Figure 3.5, where the strokes for a column of alcohol and mercury do not coincide at the same temperature.

5.2.3. Air humidity measurement

Air humidity depends on the amount of water vapor in it. For example, in the summer in the desert the air is dry and its humidity is low, since it contains little water vapor. In the subtropics, for example, in Sochi, the humidity is high and there is a lot of water vapor in the air. You can measure humidity using two thermometers. One of them is a regular one (dry bulb). The second has a ball wrapped in a damp cloth (wet thermometer). It is known that when water evaporates, body temperature decreases. (Remember the chill when you come out of the sea after swimming). Therefore, the wet bulb thermometer shows a lower temperature. The drier the air, the greater the difference between the readings of the two thermometers. If the thermometer readings are the same (the difference is zero), then the air humidity is 100%. In this case, dew falls. A device that measures air humidity is called psychrometer (Figure 3.6 ). It is equipped with a table that shows: dry bulb readings, the difference between the readings of two thermometers, and air humidity as a percentage. The closer the humidity is to 100%, the more humid the air. Normal indoor humidity should be about 60%.

Block 3.3. Self-preparation

5.3.1. Fill the table

When answering the questions in the table, fill in the empty column (“Answer”). In this case, use the pictures of devices in the “Additional” block.

760 mm. rt. Art. considered normal. Figure 3.11 shows the change in atmospheric pressure when climbing the highest mountain, Everest.

Construct a linear diagram of pressure changes, plotting height above sea level on the vertical ray and pressure along the horizontal ray.

Block 5.4. Problem

Construction of a numerical ray with a unit segment of a given length

To solve this educational problem, work according to the plan given in the left column of the table, while it is recommended to cover the right column with a sheet of paper. After answering all the questions, compare your conclusions with the solutions given.

Block 5.5. Facet test

Number beam, scale, chart

The facet test tasks used pictures from the table. All tasks begin like this: “ IF the number ray is represented in the figure...., then...»

IF: the number ray is represented in the figure... Table

The number of units between adjacent strokes of a number line.
Coordinates of points A, B, C, D.
Length (in centimeters) of segments AB, BC, AD, BD, respectively.
Length (in meters) of segments AB, BC, AD, BD, respectively.
Natural numbers located on the number line to the left of point D.
Natural numbers located on the number line between points A and C.
The number of natural numbers lying on the number line between points A and D.
The number of natural numbers lying on the number line between points B and C.
Instrument scale division price.
Vehicle speed in km/h if the speedometer needle points to points A, B, C, D, respectively.
The amount (in km/h) by which the speed of the car increased if the speedometer needle moved from point B to point C.
The speed of the car after the driver reduced the speed by 84 km/h (before reducing the speed, the speedometer needle pointed to point D).
The mass of the load on the scales in centners, if the arrow - the scale indicator - is located opposite points A, B, C, respectively.
The mass of the load on the scales in kilograms, if the arrow - the scale pointer - is located opposite points A, B, C, respectively.
The mass of the load on the scales in grams, if the arrow - the scale pointer - is located opposite points A, B, C, respectively.
Number of students in 5th grade.
The difference between the number of students achieving “4” and the number of students achieving “3”.
The ratio of the number of students achieving grades “4” and “5” to the number of students achieving grades “3”.

EQUAL (equal, equal, this):

a) 10 b) 6,12,3,3 c) 1 d) 99,102,106,104 d) 2 f) 201,202 g) 49 h) 3500,3000,8000,4500

i) 5,2,1,4 k) 599 l) 6,3,3,9 m) 10,4,16,7 n) 100 o) 4 km/h p) 65,85,105,115 p) 7,2, 4,6 c) 20,20,50,30 t) 0 y) 700,600,1600,900 f) 1,2,3,4,5,6 x) 25,10,5,20 c) 3,4, 5.2 h) 203,197,200,206 w) 15,20,25,10 w) 1599 s) 11,12,13,14,15 e) 30,60,15,15 y) 0,700,1300,1600 i) 100,100,250,150 aa) 30,15,15,45 bb) 4 vv) 1,2,3,4,5 y) 17 dd) 500 kg ee) 19 zh) 80 zz) 100,101,102,103,104,105 ii)5,6 kk) 28,64,100,164 ll) 1500000 ,3000000,4500000 mm) 11 nn) 36 oo) 1500,3000,4500 pp) 7 rr) 24 ss) 15,30,45

Block 5.6. Educational mosaic

The mosaic tasks used devices from the “Additional” block. Below is the mosaic field. The names of the devices are indicated on it. In addition, for each device the following are indicated: the measured value (V), the unit of measurement of the value (E), the instrument reading (P), the scale division value (C). Next are the mosaic cells. After reading a cell, you must first identify the device to which it belongs and put the device number in the circle of the cell. Then you need to guess what this cell is about. If we are talking about a measured quantity, you need to add a letter to the number IN. If this is a unit of measurement, put a letter E, if the instrument reading is a letter P, if the division price is a letter C. In this way, you need to designate all the cells of the mosaic. If the cells are cut out and arranged as on the field, then you can systematize information about the device. In the computer version of the mosaic, with the correct arrangement of cells, a pattern is created.

Single segment. ? A single segment can have different lengths. For example, we need to construct a coordinate ray with a unit segment equal to two cells. To do this, you need to: construct a ray (according to the rules discussed above), count two cells from point O, mark the point and give it coordinate 1, the distance from 0 to 1, equal to two cells, is a unit segment. O. 0. 1. Below is a coordinate ray with a unit segment equal to five cells. O. 0. 1.

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Mathematics 5th grade

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A unit segment is a certain quantity that has its own specific length. For example, let’s take a 40 cm ruler. This means that the ruler will have forty unit segments with a distance of 1 cm. Or 80 unit segments with a distance of 0.5 cm and so on.

A unit segment is expressed not only in centimeters, but also in inches (in most cases), kilograms, minutes, seconds, and so on.

For a detailed image of a single segment, a coordinate beam is mainly used.

A coordinate ray is a ray on which the beginning of a unit segment is specified in detail.

1 cell = 1 unit of a unit segment;
6 cells = 6;
4 cells = 4;
50 cells = 50 and so on (Fig. 1).

In geometry, and in mathematics in general, a single segment plays an important and multifunctional role. After all, on such a segment there are a lot of certain mathematical quantities. One of the main quantities is the domain of definition and the domain of value of a function.

Examples of problems with a unit segment

For example, draw a unit segment A with coordinates (6; 5) Fig. 2.

Solution: on the coordinate axis we find points 6 and 5 (that is, we count six cells and five cells). We mark these points on segment A.

Task. 12 liters of jam were divided into three-liter jars. How many of these cans did you need?

Solution: Let's construct a unit segment in accordance with the assignment. Those. Let's mark 12 cells on the coordinate axis (Fig. 3).

Then we will divide the segment into 4 parts, because According to the conditions of the problem, the jam was distributed equally.

Divide 12 / 4 = 3 (cans).

Unit segment, coordinates, number beam

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Let's draw a ray with its origin at point A.

From the beginning of the ray we will lay equal segments one after another.

At the beginning of the ray, point A, we put the number zero and renumber the ends of the segments one after the other.

This is a number beam.

The beginning of the number line corresponds to the number 0.

On the number line, any number can be represented by a dot, no matter how large it is

3, 98. "width="640"

Using the number beam it is easy to compare:

The more to the right a point is from the beginning of the ray, the larger the number it represents.

Let's secure it!

Using the number line, name all the numbers that are less than 8 and all the numbers that are greater than 8.

Write down which numbers on the number line correspond to the points A, B, C, K.

Coordinate beam

To draw a coordinate ray you need :

mark a point ABOUT – beginning of the beam at the intersection of cells;
move the beam so that it goes from left to right

Point O has coordinate 0

To build unit segment :

mark the fall point on the ray A
let's give it a point And coordinate 1

Distance from point ABOUT to the point A ,

those. the distance from 0 to 1 is unit segment .

The coordinate ray is not built if not unit segment .

Unit segment

A single segment can have different lengths

For example, we need to build a coordinate ray

With a unit segment equal to two cells

To do this you need:

build a beam (according to the rules discussed above)
count from point ABOUT two cells
mark a point and give it a coordinate 1
distance from 0 before 1 , equal to two cells

and there is unit segment

Below is a coordinate ray with single segment

equal to five cells

Coordinates

As an example of a coordinate ray we can take

an ordinary ruler.

A unit segment of a ruler is 1 cm

unit segment

Let a coordinate ray be given, unit segment whom

equals 3 cells .

Let's mark a point on it B with coordinate 3 .

To mark a point IN necessary:

from point ABOUT set aside three pieces, one after the other.

these segments must be the same length and equal to a unit segment .

at the end of the third segment mark a point IN And

give her the coordinates 3

Exercise 1

a)Draw coordinate ray With single segment,

equal to 4 cells

Check on this beam points :

A (2), WITH (1) , L (5)

b)Draw coordinate ray With single segment,

equal to 7 cells

Check on this beam points :

A (2), WITH (1), D (5)

Task 2

Dan coordinate ray

Write what it is equal to unit segment

Write coordinates of points :

To write down what the coordinate of a point is:

write the letter that represents the point
write the number corresponding to the coordinate in brackets

For example: dot A has a coordinate 1 will be written as A(1)

A single segment is usually marked on each of the axes.

Unit segment in mathematics

The role of unit in mathematics is extremely important. The unit interval, as a set of positive numbers but not exceeding one, is one of the main sets for constructing examples in all areas of mathematics.

A lot of certain mathematical quantities lie on a unit segment. For example: probability, domain of definition and domain of significance of many basic functions.

In view of this, as well as another, the operation of normalizing a set of numbers is often carried out, mapping it in various images onto a unit segment.

Single segment in crystallography

A unit segment is a segment cut off by a unit face on each of the crystallographic axes.

Unit segment A segment whose length is taken as a unit of length is called a unit segment. Which segment is called a unit segment? What is a unit segment

Mathematics 5th grade

Examples of problems with a unit segment

Unit segment in mathematics

Single segment in crystallography

see also

See what a “Single Segment” is in other dictionaries: