You will need

- and measuring devices;
- calculator.

Instruction

1

To see how much has changed or that the value, you must first find the initial and final value. If we are talking about the practical problem, the desired parameters can be measured. The setting you want is possible in principle to name any letter, but it is better to use the common science symbols. Suppose you need to find how much the volume of matter when heated. The result of the first measurement record as V1

2

Swipe the second dimension. For example, after you are done heat the object. Determine its volume and mark it as V2. Calculate

**Delta**according to the formula ΔV = V2-V1. It may happen that the second result is less than the first. Count the module numbers as well as in any other case, and put a sign "-". Don't forget that both measurements must be in the same units. If necessary, translate them.3

Frequent tasks when you need to calculate

**the Delta**between the actual and the average value. For example, you are given a point which changed their position on two axes. Label the coordinates as x1,x2, x3, etc. Find the average value. Then calculate the difference between the obtained result and the value of each coordinate.4

If you need to calculate the increment of the function f(x), define its value in a strictly specified point — let it be, for example, x0. To calculate

**the Delta**, you need to compare the value of the function at that point with its value at any other point on the given axis. To do this, subtract the value of the function at the point x1 from its value at the point x0. This will be Δf. To find the increment of the argument, determine its values at the given points and calculate the difference.5

The letter Δ and denote the absolute error. She, too, is the difference. For the initial and the final value accepted true and approximate values. The magnitude of the Delta in this case corresponds to the accuracy class of the instrument.

# Advice 2: How to calculate the volume

The volume is the space occupied by the body. To calculate the correct volume of the object, which can easily determine the parameters (length, width, height) easy. It is only necessary to multiply the found value. To determine the volume of arbitrary shapes is much more difficult.

Instruction

1

A method of measuring the volume of the object with water was open to the Greek scientist Archimedes. To determine the volume of any body need to take a container of liquid, it is better if the container is transparent. The vessel must be applied to the scale division and to measure the volume occupied by water. After that, the water should immerse the body whose volume you want to learn. As soon as the water rises, you must mark the new level. The difference in levels, obtained by measurement and is equal to the volume of the immersed body.

2

In addition, it is possible to determine the volume of the object by measuring the amount of water displaced by it. For this purpose, in a vessel brim full of water, it is necessary to load the body. With the displaced water should be poured into another container and measure the volume, which will be equal to the desired volume of the body.

3

When finding the volume of a hollow body you can also use the water. For this you need to fill it are available, subject, and then pour the water into a glass, which is applied to the scale division. The measured body volume is equal to the volume of contained water in it.

4

You can calculate the volume of any body, knowing its density and mass. It is necessary to divide the available mass of the object on its density. To know the density of the material from which made a particular item from the reference table "Density of solids".

5

To calculate some of the figures are derived mathematical formulas. For example, for finding the volume of a cylinder we need to know its radius and height. The volume of a cylinder you will receive by works of "PI" to the square of the radius and height of the body (V=π*R2*H).

# Advice 3: How to calculate absolute error

Measurements can be performed with varying degrees of accuracy. It is absolutely accurate are not even precision instruments. Absolute and relative error may be small, but in reality they are almost always. The difference between the approximate and exact values of a certain magnitude is called the absolute

**error**. The deviation can be both upwards and downwards.You will need

- - measurement data;
- calculator.

Instruction

1

Before you can calculate absolute uncertainty, take for initial data a few postulates. Eliminate gross errors. Accept that the necessary amendments have already been calculated and included in the result. The amendment may be, for example, the transfer starting point of measurement.

2

Take as a starting position that is known and taken into account random error. This implies that they are less systematic, i.e., absolute and relative, are specific to this device.

3

Random errors affect the result, even high-precision measurements. Therefore, any result will be more or less close to absolute, but there will always be differences. Determine this interval. It can be expressed by the formula (Hism - HH)≤Chism ≤ (Hism+HH).

4

*Determine the amount that approximated to the true value. In real measurements, the arithmetic mean, which can be found using the formula shown in the figure. Take the result for the true value. In many cases, as accurate a reading is taken of the reference device.*

5

Knowing the true value of the measurement, you can find the absolute error, which should be considered in all subsequent measurements. Find the value of X1 – specific data measurement. Determine the difference between the HH, subtracting a larger number from a smaller. When error determination takes into account only the module of this difference.

Note

As a rule, in practice, absolutely accurate measurement is not possible to lead. Therefore, for the reference value is taken as the limit error. It represents the maximum value of the modulus of the absolute error.

Useful advice

In practical measurements the magnitude of the absolute error is usually taken as half the smallest scale. When operating with numbers over the absolute error is taken half the value of the digit that is in the following with accurate figures for the category.

To define the accuracy class of the instrument is more important is the ratio of absolute error to the measurement result or the length scale.

To define the accuracy class of the instrument is more important is the ratio of absolute error to the measurement result or the length scale.

# Advice 4: How to calculate measurement error

The result of any measurement is inevitably accompanied by a deviation from the true value. To calculate the measurement error in several ways depending on its type, for example, statistical methods for determining the confidence interval, standard deviation, etc.

Instruction

1

There are several reasons that give rise to

**error****of measurement**. This instrument inaccuracy, imperfection techniques, as well as errors caused by inattention of the operator performing the measurements. In addition, often the true value of the parameter take its actual value, which actually is merely the most probable, based on the analysis of statistical sample results a series of experiments.2

Accuracy is a measure of the deviation of the measured parameter from its true value. According to the method of Kornfeld, determine the confidence interval, which ensures a certain degree of reliability. They find the so-called confidence limits, which varies the magnitude error is calculated as half the sum of these values:∆ = (xmax - xmin)/2.

3

This is interval estimation

**error**, which is carried out in a small volume of the statistical sample. Point estimation is to calculate the mathematical expectation and standard deviation.4

Mathematical expectation is an integral sum of a number of works by the two parameters of the observations. It actually measured value and its probability at these points:M = Σxi•pi.

5

The classic formula for calculating the standard deviation involves the calculation of the average values of the analyzed sequence of values of the measurand, and also takes into account the volume series of the experiments:σ = √(∑(xi – khsr)2/(n - 1)).

6

According to the method of expression also distinguish absolute, relative and reduced error. The absolute error is expressed in the same units as the measured value, and is equal to the difference between the estimated and true value is:∆x = x1 – x0.

7

The relative error measurements associated with the absolute, but is more efficient. It has no dimension, sometimes expressed in percentages. It is the ratio of absolute

**error**to the true or calculated value of the measured parameters:σx = ∆x/x0 or σx = ∆x/x1.8

Given the margin of error is expressed as the ratio between absolute error and some conventionally accepted value x, which is constant for all

**measurements**and is determined by the calibration of the instrument scale. If the scale starts from zero (one-sided), this normalizing value equal to its upper limit, and if a double – width of its range:σ = ∆x/xn.