How to round to units. Easy rules for rounding numbers after the decimal point

You have to round numbers more often in life than many people think. This is especially true for people in professions related to finance. People working in this field are well trained in this procedure. But also in Everyday life process converting values to integer form Not unusual. Many people conveniently forgot how to round numbers immediately after school. Let us recall the main points of this action.

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Round number

Before moving on to the rules for rounding values, it is worth understanding what is a round number. If we are talking about integers, then it must end with zero.

To the question of where in everyday life such a skill can be useful, you can safely answer - during basic shopping trips.

Using the approximate calculation rule, you can estimate how much your purchases will cost and how much you need to take with you.

It is with round numbers that it is easier to perform calculations without using a calculator.

For example, if vegetables weighing 2 kg 750 g are bought in a supermarket or market, then in a simple conversation with the interlocutor they often do not name exact weight, but they say that they purchased 3 kg of vegetables. When determining the distance between populated areas, the word “about” is also used. This means bringing the result to a convenient form.

It should be noted that some calculations in mathematics and problem solving also do not always use exact values. This is especially true in cases where the response receives infinite periodic fraction. Here are some examples where approximate values are used:

some values of constant quantities are presented in rounded form (the number “pi”, etc.);
tabular values of sine, cosine, tangent, cotangent, which are rounded to a certain digit.

Note! As practice shows, approximating values to the whole, of course, gives an error, but only an insignificant one. The higher the rank, the more accurate the result will be.

Getting approximate values

This mathematical operation is carried out according to certain rules.

But for each set of numbers they are different. Note that you can round whole numbers and decimals.

But with ordinary fractions the action is not performed.

First they need convert to decimals, and then proceed with the procedure in the required context.

The rules for approximating values are as follows:

for integers – replacing the digits following the rounded one with zeros;
for decimal fractions - discarding all numbers that are beyond the digit being rounded.

For example, rounding 303,434 to thousands, you need to replace hundreds, tens and ones with zeros, that is, 303,000. In decimals, 3.3333 rounding to the nearest ten x, simply discard all subsequent digits and get the result 3.3.

Exact rules for rounding numbers

When rounding decimals it is not enough to simply discard digits after rounded digit. You can verify this with this example. If 2 kg 150 g of sweets are purchased in a store, then they say that about 2 kg of sweets were purchased. If the weight is 2 kg 850 g, then round up to big side, that is, about 3 kg. That is, it is clear that sometimes the rounded digit is changed. When and how this is done, the exact rules will be able to answer:

If the rounded digit is followed by a digit 0, 1, 2, 3 or 4, then the rounded digit is left unchanged, and all subsequent digits are discarded.
If the digit being rounded is followed by the number 5, 6, 7, 8 or 9, then the rounded digit is increased by one, and all subsequent digits are also discarded.

For example, how to correct a fraction 7.41 bring closer to unity. Determine the number that follows the digit. In this case it is 4. Therefore, according to the rule, the number 7 is left unchanged, and the numbers 4 and 1 are discarded. That is, we get 7.

If the fraction 7.62 is rounded, then the units are followed by the number 6. According to the rule, 7 must be increased by 1, and the numbers 6 and 2 discarded. That is, the result will be 8.

The examples provided show how to round decimals to units.

Approximation to integers

It is noted that you can round to units in the same way as to round to integers. The principle is the same. Let us dwell in more detail on rounding decimal fractions to a certain digit in the whole part of the fraction. Let's imagine an example of approximating 756.247 to tens. In the tenths place there is the number 5. After the rounded place comes the number 6. Therefore, according to the rules, it is necessary to perform next steps:

rounding up tens per unit;
in the ones place, the number 6 is replaced;
digits in the fractional part of the number are discarded;
the result is 760.

Let us pay attention to some values in which the process of mathematical rounding to integers according to the rules does not reflect an objective picture. If we take the fraction 8.499, then, transforming it according to the rule, we get 8.

But in essence this is not entirely true. If we round up to whole numbers, we first get 8.5, and then we discard 5 after the decimal point and round up.

§ 4. Rounding of results

Processing of measurement results in laboratories is carried out on calculators and PCs, and it is simply amazing how magically a long series of decimal numbers works on many students. “That’s more accurate,” they think. However, it is easy to see, for example, that the entry a = 2.8674523 ± 0.076 is meaningless. With an error of 0.076, the last five digits of the number mean absolutely nothing.

If we make an error in hundredths of parts, then there is no faith in thousandths, much less ten-thousandths. A proper recording of the result would be 2.87 ± 0.08. The necessary rounding must always be done to avoid the false impression that the results are more accurate than they actually are.

Rounding rules

The measurement error is rounded to the first significant digit, always increasing by one.
Examples:
8.27 ≈ 9 0.237 ≈ 0.3
0.0862 ≈ 0.09 0.00035 ≈ 0.0004
857.3 ≈ 900 43.5 ≈ 50
The measurement results are rounded to within an error, i.e. The last significant digit of the result must be in the same place as the error.
Examples:
243.871 ± 0.026 ≈ 243.87 ± 0.03;
243.871 ± 2.6 ≈ 244 ± 3;
1053 ± 47 ≈ 1050 ± 50.
Rounding the measurement result is achieved by simply discarding digits if the first of the discarded digits is less than 5.
Examples:
8.337 (round to the nearest tenth) ≈ 8.3;
833.438 (round to whole numbers) ≈ 833;
0.27375 (round to the nearest hundredth) ≈ 0.27.
If the first digit to be discarded is greater than or equal to 5 (and one or more digits following it are non-zero), then the last remaining digit is incremented by one.
Examples:
8.3351 (round to hundredths) ≈ 8.34;
0.2510 (round to the nearest tenth) ≈ 0.3;
271.515 (round to whole numbers) ≈ 272.
If the digit to be discarded is 5 and there are no significant digits behind it (or there are only zeros), then the last digit left is increased by one when it is odd and left unchanged when it is even.
Examples:
0.875 (round to the nearest hundredth) ≈ 0.88;
0.5450 (round to the nearest hundredth) ≈ 0.54;
275.500 (round to whole numbers) ≈ 276;
276.500 (round to whole numbers) ≈ 276.

Note.

Significant numbers are the correct digits of a number, except for the zeros in front of the number. For example, 0.00807 this number has three significant figures: 8, zero between 8 and 7 and 7; the first three zeros are insignificant.
8.12 · 10 3 this number has 3 significant figures.
The entries 15.2 and 15.200 are different. The entry 15,200 means that the hundredths and thousandths are correct. In the notation 15.2 , whole and tenth parts are correct.
The results of physical experiments are recorded only in significant figures. A comma is placed immediately after a non-zero digit, and the number is multiplied by ten to the appropriate degree. Zeros at the beginning or end of a number are usually not written down. For example, the numbers 0.00435 and 234000 are written as follows: 4.35·10 -3 and 2.34·10 5 . This notation simplifies calculations, especially in the case of formulas convenient for logarithms.

Many people are interested in how to round numbers. This need often arises among people who connect their lives with accounting or other activities that require calculations. Rounding can be done to whole numbers, tenths, and so on. And you need to know how to do it correctly so that the calculations are more or less accurate.

What is a round number anyway? This is the one that ends in 0 (for the most part). In everyday life, the ability to round numbers makes shopping trips much easier. Standing at the cash register, you can roughly estimate total cost shopping, compare how much a kilogram of the same product costs in packages of different weights. With numbers reduced to convenient form, it is easier to make verbal calculations without resorting to a calculator.

Why are numbers rounded?

People tend to round any numbers in cases where it is necessary to perform more simplified operations. For example, a melon weighs 3,150 kilograms. When a person tells his friends about how many grams the southern fruit has, he may be considered a not very interesting interlocutor. Phrases like “So I bought a three-kilogram melon” sound much more concise without delving into all sorts of unnecessary details.

Interestingly, even in science there is no need to always deal with the most accurate numbers possible. But if we are talking about periodic infinite fractions, which have the form 3.33333333...3, then this becomes impossible. Therefore, the most logical option would be to simply round them. As a rule, the result is then slightly distorted. So how do you round numbers?

Some important rules when rounding numbers

So, if you wanted to round a number, is it important to understand the basic principles of rounding? This is a modification operation aimed at reducing the number of decimal places. To perform this action, you need to know a few important rules:

If the number of the required digit is in the range of 5-9, rounding is carried out upward.
If the number of the required digit is in the range 1-4, rounding is done downwards.

For example, we have the number 59. We need to round it. To do this, you need to take the number 9 and add one to it to get 60. This is the answer to the question of how to round numbers. Now let's look at special cases. Actually, we figured out how to round a number to tens using this example. Now all that remains is to use this knowledge in practice.

How to round a number to whole numbers

It often happens that there is a need to round, for example, the number 5.9. This procedure is not a big deal. First we need to omit the comma, and when we round, the already familiar number 60 appears before our eyes. Now we put the comma in place, and we get 6.0. And since zeros in decimal fractions are usually omitted, we end up with the number 6.

A similar operation can be performed with more complex numbers. For example, how do you round numbers like 5.49 to integers? It all depends on what goals you set for yourself. In general, according to the rules of mathematics, 5.49 is still not 5.5. Therefore, it cannot be rounded up. But you can round it up to 5.5, after which it becomes legal to round up to 6. But this trick doesn’t always work, so you need to be extremely careful.

In principle, an example of correct rounding of a number to tenths has already been discussed above, so now it is important to display only the main principle. Essentially, everything happens in approximately the same way. If the digit that is in the second position after the decimal point is in the range 5-9, then it is removed altogether, and the digit in front of it is increased by one. If it is less than 5, then this figure is removed, and the previous one remains in its place.

For example, at 4.59 to 4.6, the number “9” disappears, and one is added to the five. But when rounding 4.41, the unit is omitted, and the four remains unchanged.

How do marketers take advantage of the mass consumer's inability to round numbers?

It turns out that most people in the world do not have the habit of assessing the real cost of a product, which is actively exploited by marketers. Everyone knows promotion slogans like “Buy for only 9.99.” Yes, we consciously understand that this is essentially ten dollars. Nevertheless, our brain is designed in such a way that it perceives only the first digit. So the simple operation of bringing a number into a convenient form should become a habit.

Very often, rounding allows you to better evaluate intermediate successes expressed in numerical form. For example, a person began to earn $550 a month. An optimist will say that it is almost 600, a pessimist will say that it is a little more than 500. It seems that there is a difference, but it is more pleasant for the brain to “see” that the object has achieved something more (or vice versa).

There are a huge number of examples where the ability to round turns out to be incredibly useful. It's important to be creative and stay busy whenever possible. unnecessary information. Then success will be immediate.

Today we will look at a rather boring topic, without understanding which it is not possible to move on. This topic is called “rounding numbers” or in other words “approximate values of numbers.”

Lesson content

Approximate values

Approximate (or approximate) values are used when the exact value of something cannot be found, or the value is not important to the item being examined.

For example, in words one can say that half a million people live in a city, but this statement will not be true, since the number of people in the city changes - people come and leave, are born and die. Therefore, it would be more correct to say that the city lives approximately half a million people.

Another example. Classes start at nine in the morning. We left the house at 8:30. After some time on the road, we met a friend who asked us what time it was. When we left the house it was 8:30, we spent some unknown time on the road. We don’t know what time it is, so we answer our friend: “now approximately about nine o'clock."

In mathematics, approximate values are indicated using a special sign. It looks like this:

Read as "approximately equal."

To indicate the approximate value of something, they resort to such an operation as rounding numbers.

Rounding numbers

To find an approximate value, an operation such as rounding numbers.

The word "rounding" speaks for itself. To round a number means to make it round. A number that ends in zero is called round. For example, the following numbers are round,

10, 20, 30, 100, 300, 700, 1000

Any number can be made round. The procedure by which a number is made round is called rounding the number.

We have already been involved in “rounding” numbers when we divided big numbers. Let us recall that for this we left the digit forming the most significant digit unchanged, and replaced the remaining digits with zeros. But these were just sketches that we made to make division easier. A kind of life hack. In fact, this was not even a rounding of numbers. That is why at the beginning of this paragraph we put the word rounding in quotation marks.

In fact, the essence of rounding is to find the closest value from the original. At the same time, the number can be rounded to a certain digit - to the tens digit, the hundreds digit, the thousand digit.

Let's look at a simple example of rounding. Given the number 17. You need to round it to the tens place.

Without getting ahead of ourselves, let’s try to understand what “round to the tens place” means. When they say to round the number 17, we are required to find the nearest round number for the number 17. Moreover, during this search, changes may also affect the number that is in the tens place in the number 17 (i.e., ones).

Let's imagine that all numbers from 10 to 20 lie on a straight line:

The figure shows that for the number 17 the nearest round number is 20. So the answer to the problem will be like this: 17 is approximately equal to 20

17 ≈ 20

We found an approximate value for 17, that is, we rounded it to the tens place. It can be seen that after rounding, a new digit 2 appeared in the tens place.

Let's try to find an approximate number for the number 12. To do this, imagine again that all numbers from 10 to 20 lie on a straight line:

The figure shows that the nearest round number for 12 is the number 10. So the answer to the problem will be like this: 12 is approximately equal to 10

12 ≈ 10

We found an approximate value for 12, that is, we rounded it to the tens place. This time the number 1, which was in the tens place in the number 12, did not suffer from rounding. We will look at why this happened later.

Let's try to find the closest number for the number 15. Let's imagine again that all numbers from 10 to 20 lie on a straight line:

The figure shows that the number 15 is equally distant from the round numbers 10 and 20. The question arises: which of these round numbers will be the approximate value for the number 15? For such cases, we agreed to take the larger number as an approximate one. 20 is greater than 10, so the approximation for 15 is 20

15 ≈ 20

Large numbers can also be rounded. Naturally, it is not possible for them to draw a straight line and depict numbers. There is a way for them. For example, let's round the number 1456 to the tens place.

We must round 1456 to the tens place. The tens place begins at five:

Now we temporarily forget about the existence of the first numbers 1 and 4. The number remaining is 56

Now we look at which round number is closer to the number 56. Obviously, the closest round number for 56 is the number 60. So we replace the number 56 with the number 60

So, when rounding the number 1456 to the tens place, we get 1460

1456 ≈ 1460

It can be seen that after rounding the number 1456 to the tens place, the changes affected the tens place itself. The new number obtained now has a 6 in the tens place, not a 5.

You can round numbers not only to the tens place. You can also round to the hundreds, thousands, or tens of thousands place.

Once it becomes clear that rounding is nothing more than searching for the nearest number, you can apply ready-made rules that make rounding numbers much easier.

First rounding rule

From the previous examples it became clear that when rounding a number to a certain digit, the low-order digits are replaced by zeros. Numbers that are replaced by zeros are called discarded digits.

The first rounding rule is as follows:

If, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

For example, let's round the number 123 to the tens place.

First of all, we find the digit to be stored. To do this, you need to read the task itself. The digit being stored is located in the digit referred to in the task. The assignment says: round the number 123 to tens place.

We see that there is a two in the tens place. So the stored digit is 2

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after the two is the number 3. This means the number 3 is first digit to be discarded.

Now we apply the rounding rule. It says that if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

That's what we do. We leave the stored digit unchanged, and replace all low-order digits with zeros. In other words, we replace everything that follows the number 2 with zeros (more precisely, zero):

123 ≈ 120

This means that when rounding the number 123 to the tens place, we get the number 120 approximating it.

Now let's try to round the same number 123, but to hundreds place.

We need to round the number 123 to the hundreds place. Again we are looking for the number to be saved. This time the digit being stored is 1 because we are rounding the number to the hundreds place.

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after one is the number 2. This means that the number 2 is first digit to be discarded:

Now let's apply the rule. It says that if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

That's what we do. We leave the stored digit unchanged, and replace all low-order digits with zeros. In other words, we replace everything that follows the number 1 with zeros:

123 ≈ 100

This means that when rounding the number 123 to the hundreds place, we get the approximate number 100.

Example 3. Round 1234 to the tens place.

Here the retained digit is 3. And the first discarded digit is 4.

This means we leave the saved number 3 unchanged, and replace everything that is located after it with zero:

1234 ≈ 1230

Example 4. Round 1234 to the hundreds place.

Here, the retained digit is 2. And the first discarded digit is 3. According to the rule, if, when rounding numbers, the first of the discarded digits is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means we leave the saved number 2 unchanged, and replace everything that is located after it with zeros:

1234 ≈ 1200

Example 3. Round 1234 to the thousands place.

Here, the retained digit is 1. And the first discarded digit is 2. According to the rule, if, when rounding numbers, the first of the discarded digits is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means we leave the saved digit 1 unchanged, and replace everything that is located after it with zeros:

1234 ≈ 1000

Second rounding rule

The second rounding rule is as follows:

When rounding numbers, if the first digit to be discarded is 5, 6, 7, 8, or 9, then the retained digit is increased by one.

For example, let's round the number 675 to the tens place.

We see that there is a seven in the tens place. So the digit being stored is 7

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after seven is the number 5. This means that the number 5 is first digit to be discarded.

Our first discarded digit is 5. This means we must increase the retained digit 7 by one, and replace everything after it with zero:

675 ≈ 680

This means that when rounding the number 675 to the tens place, we obtain the approximate number 680.

Now let's try to round the same number 675, but to hundreds place.

We need to round the number 675 to the hundreds place. Again we are looking for the number to be saved. This time the digit being stored is 6, since we are rounding the number to the hundreds place:

Now we find the first of the discarded digits. The first digit to be discarded is the digit that comes after the digit to be stored. We see that the first digit after six is the number 7. This means that the number 7 is first digit to be discarded:

Now we apply the second rounding rule. It says that when rounding numbers, if the first digit to be discarded is 5, 6, 7, 8, or 9, then the digit retained is increased by one.

Our first discarded digit is 7. This means we must increase the retained digit 6 by one, and replace everything after it with zeros:

675 ≈ 700

This means that when rounding the number 675 to the hundreds place, we get the approximate number 700.

Example 3. Round the number 9876 to the tens place.

Here the retained digit is 7. And the first discarded digit is 6.

This means we increase the stored number 7 by one, and replace everything that is located after it with zero:

9876 ≈ 9880

Example 4. Round 9876 to the hundreds place.

Here the retained digit is 8. And the first discarded digit is 7. According to the rule, if, when rounding numbers, the first of the discarded digits is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means we increase the stored number 8 by one, and replace everything that is located after it with zeros:

9876 ≈ 9900

Example 5. Round 9876 to the thousands place.

Here, the retained digit is 9. And the first discarded digit is 8. According to the rule, if, when rounding numbers, the first of the discarded digits is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means we increase the stored number 9 by one, and replace everything that is located after it with zeros:

9876 ≈ 10000

Example 6. Round 2971 to the nearest hundred.

When rounding this number to the nearest hundred, you should be careful because the digit being retained here is 9, and the first digit to be discarded is 7. This means that the digit 9 must be increased by one. But the fact is that after increasing nine by one, the result is 10, and this figure will not fit into the hundreds digit of the new number.

In this case, in the hundreds place of the new number you need to write 0, and move the unit to the next place and add it with the number that is there. Next, replace all digits after the saved one with zeros:

2971 ≈ 3000

Rounding decimals

When rounding decimal fractions, you should be especially careful because a decimal fraction consists of an integer part and a fractional part. And each of these two parts has its own categories:

Integer digits:

units digit
tens place
hundreds place
thousand digit

Fractional digits:

tenth place
hundredths place
thousandth place

Let's consider decimal 123.456 - one hundred twenty-three point four hundred fifty-six thousandths. Here the integer part is 123, and the fractional part is 456. Moreover, each of these parts has its own digits. It is very important not to confuse them:

For the integer part, the same rounding rules apply as for regular numbers. The difference is that after rounding the integer part and replacing all digits after the stored digit with zeros, the fractional part is completely discarded.

For example, round the fraction 123.456 to tens place. Exactly until tens place, but not tenth place. It is very important not to confuse these categories. Discharge dozens is located in the whole part, and the digit tenths in fractional

We must round 123.456 to the tens place. The digit retained here is 2, and the first digit discarded is 3

According to the rule, if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means that the saved digit will remain unchanged, and everything else will be replaced by zero. What to do with the fractional part? It is simply discarded (removed):

123,456 ≈ 120

Now let's try to round the same fraction 123.456 to units digit. The digit to be retained here will be 3, and the first digit to be discarded is 4, which is in the fractional part:

According to the rule, if, when rounding numbers, the first digit to be discarded is 0, 1, 2, 3 or 4, then the retained digit remains unchanged.

This means that the saved digit will remain unchanged, and everything else will be replaced by zero. The remaining fractional part will be discarded:

123,456 ≈ 123,0

The zero that remains after the decimal point can also be discarded. So the final answer will look like this:

123,456 ≈ 123,0 ≈ 123

Now let's start rounding fractional parts. The same rules apply for rounding fractional parts as for rounding whole parts. Let's try to round the fraction 123.456 to tenth place. The number 4 is in the tenths place, which means it is the retained digit, and the first digit to be discarded is 5, which is in the hundredths place:

According to the rule, when rounding numbers, if the first digit to be discarded is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means that the stored digit 4 will increase by one, and the rest will be replaced by zeros

123,456 ≈ 123,500

Let's try to round the same fraction 123.456 to the hundredth place. The digit retained here is 5, and the first digit discarded is 6, which is in the thousandths place:

According to the rule, when rounding numbers, if the first digit to be discarded is 5, 6, 7, 8 or 9, then the retained digit is increased by one.

This means that the stored digit 5 will increase by one, and the rest will be replaced by zeros

123,456 ≈ 123,460

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When rounding, only the correct signs are retained, the rest are discarded.

Rule 1: Rounding is achieved by simply discarding digits if the first digit to be discarded is less than 5.

Rule 2. If the first of the discarded digits is greater than 5, then the last digit is increased by one. The last digit is also incremented when the first digit to be discarded is 5, followed by one or more non-zero digits. For example, various roundings of 35.856 would be 35.86; 35.9; 36.

Rule 3. If the discarded digit is 5, and there are no significant digits behind it, then rounding is done to the nearest even number, i.e. the last digit stored remains unchanged if it is even and increases by one if it is odd. For example, 0.435 is rounded to 0.44; We round 0.465 to 0.46.

8. EXAMPLE OF PROCESSING MEASUREMENT RESULTS

Determination of density of solids. Suppose solid has the shape of a cylinder. Then the density ρ can be determined by the formula:

where D is the diameter of the cylinder, h is its height, m is mass.

Let the following data be obtained as a result of measurements of m, D, and h:

No.	m, g	Δm, g	D, mm	ΔD, mm	h, mm	Δh, mm	, g/cm 3	Δ, g/cm 3
	51,2	0,1	12,68	0,07	80,3	0,15	5,11	0,07	0,013
	12,63	80,2
	12,52	80,3
	12,59	80,2
	12,61	80,1
average			12,61		80,2		5,11

Let's determine the average value of D̃:

Let's find the errors of individual measurements and their squares

Let us determine the root mean square error of a series of measurements:

We set the reliability value α = 0.95 and use the table to find the Student coefficient t α. n =2.8 (for n = 5). We determine the boundaries of the confidence interval:

Since the calculated value ΔD = 0.07 mm significantly exceeds the absolute micrometer error of 0.01 mm (measurement is made with a micrometer), the resulting value can serve as an estimate of the confidence interval limit:

D = D̃ ± Δ D; D= (12.61 ±0.07) mm.

Let's determine the value of h̃:

Hence:

For α = 0.95 and n = 5 Student's coefficient t α, n = 2.8.

Determining the boundaries of the confidence interval

Since the obtained value Δh = 0.11 mm is of the same order as the caliper error, equal to 0.1 mm (h is measured with a caliper), the boundaries of the confidence interval should be determined by the formula:

Hence:

Let's calculate the average density ρ:

Let's find an expression for the relative error:

Where

7. GOST 16263-70 Metrology. Terms and Definitions.

8. GOST 8.207-76 Direct measurements with multiple observations. Methods for processing observation results.

9. GOST 11.002-73 (Article CMEA 545-77) Rules for assessing the anomaly of observation results.

Tsarkovskaya Nadezhda Ivanovna

Sakharov Yuri Georgievich

General physics

Guidelines for implementation laboratory work“Introduction to the theory of measurement errors” for students of all specialties

Format 60*84 1/16 Volume 1 academic publication. l. Circulation 50 copies.

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8.27 ≈ 9	0.237 ≈ 0.3
0.0862 ≈ 0.09	0.00035 ≈ 0.0004
857.3 ≈ 900	43.5 ≈ 50