5 is rounded up. Rounding numbers

Numbers are also rounded to other digits - tenths, hundredths, tens, hundreds, etc.

If the number is rounded to some digit, then all the digits following this digit are replaced with zeros, and if they are after the decimal point, then they are discarded.

Rule number 1. If the first of the discarded digits is greater than or equal to 5, then the last of the retained digits is amplified, that is, increased by one.

Example 1. Given the number 45.769, which must be rounded to tenths. The first discarded digit is 6 ˃ 5. Consequently, the last of the stored digits (7) is amplified, i.e., increased by one. And so the rounded number would be 45.8.

Example 2. Given the number 5.165, which must be rounded to hundredths. The first discarded digit is 5 = 5. Therefore, the last of the stored digits (6) is amplified, that is, it increases by one. And so the rounded number would be 5.17.

Rule number 2. If the first of the discarded digits is less than 5, then no gain is made.

Example: The number 45.749 is given and needs to be rounded to tenths. The first discarded digit is 4

Rule number 3. If the discarded digit is 5, and there is no after it significant figures then rounding up to the nearest even number. That is, the last digit remains unchanged if it is even and increases if it is odd.

Example 1: Rounding the number 0.0465 to the third decimal place, we write - 0.046. We do not make amplifications, because the last saved digit (6) is even.

Example 2. Rounding the number 0.0415 to the third decimal place, we write - 0.042. We make amplifications, because the last saved digit (1) is odd.

In some cases, the exact number when dividing a certain amount by a specific number cannot be determined in principle. For example, when dividing 10 by 3, we get 3.3333333333…..3, that is, this number cannot be used to count specific items in other situations. Then the given number should be reduced to a certain digit, for example, to an integer or to a number with a decimal place. If we convert 3.3333333333…..3 to an integer, we get 3, and if we convert 3.3333333333…..3 to a number with a decimal place, we get 3.3.

Rounding rules

What is rounding? This is the discarding of several digits that are the last in a series of exact numbers. So, following our example, we discarded all the last digits to get an integer (3) and discarded the digits, leaving only the tens digits (3,3). The number can be rounded to hundredths and thousandths, ten thousandths and other numbers. It all depends on how accurate the number needs to be. For example, in the manufacture of medicines, the amount of each of the ingredients of the drug is taken with the greatest accuracy, since even a thousandth of a gram can be fatal. If it is necessary to calculate the performance of students at school, then most often a number with a decimal or hundredth place is used.

Let's look at another example that uses rounding rules. For example, there is a number 3.583333, which must be rounded to thousandths - after rounding, we should have three digits behind the comma, that is, the result will be the number 3.583. If this number is rounded to tenths, then we get not 3.5, but 3.6, since after “5” there is the number “8”, which is already equal to “10” during rounding. Thus, following the rules for rounding numbers, you need to know that if the digits are greater than "5", then the last digit to be stored will be increased by 1. If there is a digit less than "5", the last stored digit remains unchanged. Such rules for rounding numbers apply regardless of whether they are up to an integer or up to tens, hundredths, etc. you need to round the number.

In most cases, if it is necessary to round a number in which the last digit is "5", this process is not performed correctly. But there is also a rounding rule that applies to just such cases. Let's look at an example. You need to round the number 3.25 to tenths. Applying the rules for rounding numbers, we get the result 3.2. That is, if after "five" there is no digit or there is zero, then the last digit remains unchanged, but only on condition that it is even - in our case, "2" is an even digit. If we were to round 3.35, the result would be 3.4. Since, in accordance with the rounding rules, if there is an odd digit before the “5” that needs to be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after the “5”. In many cases, simplified rules can be applied, according to which, if there are digits from 0 to 4 after the last stored digit, the stored digit does not change. If there are other digits, the last digit is incremented by 1.

Today we will consider 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 apply when exact value it is impossible to find anything, or this value is not important for the object under study.

For example, one can verbally 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 go, 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. Some time later, on the way, we met our 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 a friend: “now approximately around nine o'clock."

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

It is 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 round number is a number that ends in zero. For example, the following numbers are round,

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

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

We have already dealt with the "rounding" of numbers when dividing big numbers. Recall that for this we left the digit forming the most significant digit unchanged, and replaced the remaining digits with zeros. But these were only sketches that we made to facilitate division. Kind of a hack. In fact, it wasn't even rounding numbers. That is why at the beginning of this paragraph we took the word rounding in quotation marks.

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

Consider a simple rounding example. The number 17 is given. It is required to round it up to the digit of tens.

Without looking ahead, let's try to understand what it means to "round to the digit of tens." When they say to round the number 17, we are required to find the nearest round number for the number 17. At the same time, during this search, the number that is in the tens place in the number 17 (i.e. units) may also be changed.

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 number 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 of 12, was not affected by rounding. Why this happened, we will consider later.

Let's try to find the nearest number to the number 15. Again, imagine 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 an approximate value for the number 15? For such cases, we agreed to take a larger number as an approximation. 20 is greater than 10, so the approximate value for 15 is the number 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 have to round 1456 to the tens place. The tens digit starts at five:

Now we temporarily forget about the existence of the first digits 1 and 4. The number 56 remains

Now we look at which round number is closer to the number 56. Obviously, the nearest 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 digit, the changes also affected the tens digit itself. The new resulting number now has a 6 instead of a 5 in the tens place.

You can round numbers not only to the digit of tens. You can also round up to the discharge of hundreds, thousands, tens of thousands.

After it becomes clear that rounding is nothing more than finding 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 lower digits are replaced by zeros. Digits that are replaced by zeros are called discarded figures.

The first rounding rule looks like this:

If, when rounding numbers, the first of the discarded digits is 0, 1, 2, 3, or 4, then the stored digit remains unchanged.

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

First of all, we find the stored digit. To do this, you need to read the task itself. In the discharge, which is mentioned in the task, there is a stored figure. The task says: round the number 123 up to tens digit.

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

Now we find the first of the discarded digits. The first digit to be discarded is the digit that follows the digit to be retained. We see that the first digit after the two is the number 3. So the number 3 is first discarded digit.

Now apply the rounding rule. It says that if, when rounding numbers, the first of the discarded digits is 0, 1, 2, 3, or 4, then the stored digit remains unchanged.

So we do. We leave the stored digit unchanged, and replace all the lower digits with zeros. In other words, everything that follows after the number 2 is replaced by zeros (more precisely, zero):

123 ≈ 120

So when rounding the number 123 to the digit of tens, we get the approximate number 120.

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

We need to round the number 123 to the hundreds place. Again we are looking for a saved figure. This time, the stored digit 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 follows the digit to be retained. We see that the first digit after the unit is the number 2. So the number 2 is first discarded digit:

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

So we do. We leave the stored digit unchanged, and replace all the lower digits with zeros. In other words, everything that follows after the number 1 is replaced with zeros:

123 ≈ 100

So when rounding the number 123 to the hundreds place, we get the approximate number 100.

Example 3 Round the number 1234 to the tens place.

Here the digit to be kept is 3. And the first digit to be discarded is 4.

So we leave the saved number 3 unchanged, and replace everything after it with zero:

1234 ≈ 1230

Example 4 Round the number 1234 to the hundreds place.

Here, the stored 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 stored digit remains unchanged.

So we leave the saved number 2 unchanged, and replace everything after it with zeros:

1234 ≈ 1200

Example 3 Round the number 1234 to the thousandth place.

Here, the stored 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 stored digit remains unchanged.

So we leave the saved number 1 unchanged, and replace everything after it with zeros:

1234 ≈ 1000

Second rounding rule

The second rounding rule looks like this:

If, when rounding numbers, the first of the discarded digits is 5, 6, 7, 8, or 9, then the stored digit is increased by one.

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

We see that in the category of tens there is a seven. So the stored digit is the number 7

Now we find the first of the discarded digits. The first digit to be discarded is the digit that follows the digit to be retained. We see that the first digit after the seven is the number 5. So the number 5 is first discarded digit.

We have the first of the discarded digits is 5. So we must increase the stored digit 7 by one, and replace everything after it with zero:

675 ≈ 680

So when rounding the number 675 to the digit of tens, we get the approximate number 680.

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

We need to round the number 675 to the hundreds place. Again we are looking for a saved figure. This time, the stored digit is 6, because we're 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 follows the digit to be retained. We see that the first digit after the six is the number 7. So the number 7 is first discarded digit:

Now apply the second rounding rule. It says that 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.

We have the first of the discarded digits is 7. So we must increase the stored digit 6 by one, and replace everything after it with zeros:

675 ≈ 700

So when rounding the number 675 to the hundreds place, we get the number 700 approximate to it.

Example 3 Round the number 9876 to the tens place.

Here the digit to be kept is 7. And the first digit to be discarded is 6.

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

9876 ≈ 9880

Example 4 Round the number 9876 to the hundreds place.

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

So we increase the saved number 8 by one, and replace everything that is located after it with zeros:

9876 ≈ 9900

Example 5 Round the number 9876 to the thousandth place.

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

So we increase the saved number 9 by one, and replace everything that is located after it with zeros:

9876 ≈ 10000

Example 6 Round the number 2971 to the nearest hundred.

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

In this case, in the hundreds place of the new number, you need to write 0, and transfer the unit to the next digit and add it to the number that is there. Next, replace all digits after the stored zero:

2971 ≈ 3000

Rounding decimals

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

Bits of the integer part:

unit digit
tens place
hundreds place
thousand digit

Fractional digits:

tenth place
hundredth place
thousandth place

Consider the decimal fraction 123.456 - one hundred and twenty-three point four hundred and fifty-six thousandths. Here whole part this 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, let's round the fraction 123.456 to tens digit. Exactly up to tens place, but not tenth place. It is very important not to confuse these categories. Discharge dozens is located in the integer part, and the discharge tenths in fractional.

We have to round 123.456 to the tens place. The digit to be stored here is 2 and the first digit to be discarded 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 that the stored digit will remain unchanged, and everything else will be replaced by zero. What about the fractional part? It is simply discarded (removed):

123,456 ≈ 120

Now let's try to round the same fraction 123.456 up to unit digit. The digit to be stored 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 of the discarded digits is 0, 1, 2, 3, or 4, then the retained digit remains unchanged.

This means that the stored 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 take a look at the rounding of 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. In the tenth place is the number 4, which means it is the stored digit, and the first discarded digit is 5, which is in the hundredth place:

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.

So the stored number 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 stored here is 5, and the first digit to discard is 6, which is in the thousandths place:

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.

So the stored number 5 will increase by one, and the rest will be replaced by zeros

123,456 ≈ 123,460

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Many people wonder how to round numbers. This need often arises for people who connect their lives with accounting or other activities that require calculations. Rounding can be done to integers, 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? It's the one that ends in 0 (for the most part). AT everyday life the ability to round numbers greatly facilitates shopping trips. Standing at the checkout, you can roughly estimate the total cost of purchases, compare how much a kilogram of the same product costs in packages of different weights. With numbers reduced to a convenient form, it is easier to make mental calculations without resorting to the help of a calculator.

Why are numbers rounded up?

A person tends to round any numbers in cases where more simplified operations need to be performed. For example, a melon weighs 3,150 kilograms. When a person tells his friends about how many grams a southern fruit has, he may be considered not a 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. And 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 after that is distorted slightly. So how do you round numbers?

Some important rules for rounding numbers

So, if you want to round a number, is it important to understand the basic principles of rounding? This is a change 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 up is carried out.
If the number of the desired digit is between 1-4, rounding down is performed.

For example, we have the number 59. We need to round it up. To do this, you need to take the number 9 and add one to it to get 60. That's the answer to the question of how to round numbers. Now let's consider special cases. Actually, we figured out how to round a number to tens using this example. Now it remains only to put this knowledge into practice.

How to round a number to integers

It often happens that there is a need to round, for example, the number 5.9. This procedure is not difficult. First we need to omit the comma, and when rounding, the already familiar number 60 appears before our eyes. And now we put the comma in place, and we get 6.0. And since the zeros in decimal fractions, as a rule, are omitted, then 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 rounding up to 6 becomes legal. But this trick does not always work, so you need to be extremely careful.

In principle, an example of the correct rounding of a number to tenths has already been considered above, so now it is important to display only the main principle. In fact, everything happens in approximately the same way. If the digit that is in the second position after the decimal point is within 5-9, then it is generally removed, and the digit in front of it is increased by one. If 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" goes away, and one is added to the five. But when rounding 4.41, the unit is omitted, and the four remains unchanged.

How do marketers use the inability of the mass consumer to round numbers?

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

Very often, rounding allows a better estimate of intermediate successes, expressed in numerical form. For example, a person began to earn $ 550 a month. An optimist will say that this is almost 600, a pessimist - 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 countless examples where the ability to round is incredibly useful. It is important to be creative and, if possible, not to be loaded with unnecessary information. Then success will be immediate.

In approximate calculations, it is often necessary to round some numbers, both approximate and exact, that is, to remove one or more final digits. In order to ensure that a single rounded number is as close as possible to the number being rounded, certain rules must be followed.

If the first of the separated digits is greater than the number 5, then the last of the remaining digits is strengthened, in other words, it increases by one. Gain is also assumed when the first of the removed digits is 5 , followed by one or more significant digits.

The number 25.863 is rounded off as - 25.9. In this case, the digit 8 will be strengthened to 9 , since the first cut off digit 6 is greater than 5 .

The number 45.254 is rounded off as - 45.3. Here, the digit 2 will be boosted to 3 because the first digit to cut off is 5 , followed by the significant digit 1 .

If the first of the cut off digits is less than 5 , then no amplification is performed.

The number 46.48 is rounded off as - 46. The number 46 is closest to the rounded number than 47 .

If the digit 5 is cut off, and there are no significant digits behind it, then rounding is performed to the nearest even number, in other words, the last remaining digit remains unchanged if it is even, and amplifies if it is odd.

The number 0.0465 is rounded off as - 0.046. In this case, no amplification is done, since the last remaining digit 6 is even.

The number 0.935 is rounded off as - 0.94. The last digit left, 3, is reinforced because it is odd.

Rounding numbers

Numbers are rounded when full precision is not needed or possible.

Round number to a certain digit (sign), it means to replace it with a number close in value with zeros at the end.

Natural numbers are rounded up to tens, hundreds, thousands, etc. Names of numbers in digits natural number you can remember in the topic of natural numbers.

Depending on the digit to which the number should be rounded, we replace the digit with zeros in the digits of units, tens, etc.

If the number is rounded to tens, then zeros replace the digit in the unit digit.

If a number is rounded to the nearest hundred, then zero must be in both the units and tens places.

The number obtained by rounding is called the approximate value of this number.

Record the rounding result after the special sign "≈". This sign is read as "approximately equal".

When rounding a natural number to some digit, you must use rounding rules.

Underline the digit to which you want to round the number.
Separate all digits to the right of this digit with a vertical bar.
If the number 0, 1, 2, 3 or 4 is to the right of the underlined digit, then all digits that are separated to the right are replaced by zeros. The digit of the category to which rounding is left unchanged.
If to the right of the underlined digit is the number 5, 6, 7, 8 or 9, then all the digits that are separated to the right are replaced by zeros, and 1 is added to the digit of the digit to which they were rounded.

Let's explain with an example. Let's round 57,861 to the nearest thousand. Let's follow the first two points from the rounding rules.

After the underlined digit is the number 8, so we add 1 to the thousands digit (we have it 7), and replace all the digits separated by a vertical bar with zeros.

Now let's round 756,485 to the nearest hundred.

Let's round 364 to tens.

3 6 |4 ≈ 360 - there is 4 in the units place, so we leave 6 in the tens place unchanged.

On the numerical axis, the number 364 is enclosed between two "round" numbers 360 and 370. These two numbers are called approximate values of the number 364 with an accuracy of tens.

The number 360 is approximate deficient value, and the number 370 is approximate excess value.

In our case, rounding 364 to tens, we got 360 - an approximate value with a disadvantage.

Rounded results are often written without zeros, adding the abbreviations "thousands." (thousand), "million" (million) and "billion." (billion).

8,659,000 = 8,659 thousand
3,000,000 = 3 million

Rounding is also used to roughly check the answer in calculations.

Before an exact calculation, we will estimate the answer by rounding the factors to the highest digit.

794 52 ≈ 800 50 ≈ 40,000

We conclude that the answer will be close to 40,000 .

794 52 = 41 228

Similarly, you can perform an estimate by rounding and when dividing numbers.

Rounding rules

Let's look at another example that uses rounding rules. For example, there is a number 3.583333, which must be rounded to thousandths - after rounding, we should have three digits behind the decimal point, that is, the result will be the number 3.583. If this number is rounded to tenths, then we get not 3.5, but 3.6, since after “5” there is the number “8”, which is already equal to “10” during rounding. Thus, following the rules for rounding numbers, you need to know that if the digits are greater than "5", then the last digit to be stored will be increased by 1. If there is a digit less than "5", the last stored digit remains unchanged. Such rules for rounding numbers apply regardless of whether they are up to an integer or up to tens, hundredths, etc. you need to round the number.

In most cases, if it is necessary to round a number in which the last digit is "5", this process is not performed correctly. But there is also a rounding rule that applies to just such cases. Let's look at an example. You need to round the number 3.25 to tenths. Applying the rules for rounding numbers, we get the result 3.2. That is, if there is no digit after “five” or there is zero, then the last digit remains unchanged, but only on condition that it is even - in our case, “2” is an even digit. If we were to round 3.35, the result would be 3.4. Since, in accordance with the rounding rules, if there is an odd digit before the “5” that needs to be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after the “5”. In many cases, simplified rules can be applied, according to which, if there are digits from 0 to 4 after the last stored digit, the stored digit does not change. If there are other digits, the last digit is incremented by 1.

5.5.7. Rounding numbers

To round a number to a certain digit, we underline the digit of this digit, and then we replace all the digits behind the underlined one with zeros, and if they are after the decimal point, we discard. If the first zero-replaced or discarded digit is 0, 1, 2, 3 or 4, then the underlined number leave unchanged. If the first zero-replaced or discarded digit is 5, 6, 7, 8 or 9, then the underlined number increase by 1.

Examples.

Round to whole:

1) 12,5; 2) 28,49; 3) 0,672; 4) 547,96; 5) 3,71.

Decision. We underline the number in the units (integer) category and look at the number behind it. If this is the number 0, 1, 2, 3 or 4, then the underlined number is left unchanged, and all the numbers after it are discarded. If the underlined number is followed by the number 5 or 6 or 7 or 8 or 9, then the underlined number will be increased by one.

1) 1 2 ,5≈13;

2) 2 8 ,49≈28;

3) 0 ,672≈1;

4) 54 7 ,96≈548;

5) 3 ,71≈4.

Round to tenths:

6) 0, 246; 7) 41,253; 8) 3,81; 9) 123,4567; 10) 18,962.

Decision. We underline the number that is in the category of tenths, and then we act according to the rule: we will discard all those after the underlined number. If the underlined digit was followed by the number 0 or 1 or 2 or 3 or 4, then the underlined digit is not changed. If the underlined number was followed by the number 5 or 6 or 7 or 8 or 9, then the underlined number will be increased by 1.

6) 0, 2 46≈0,2;

7) 41, 2 53≈41,3;

8) 3, 8 1≈3,8;

9) 123, 4 567≈123,5;

10) 18, 9 62≈19.0. There is a six behind the nine, therefore, we increase the nine by 1. (9 + 1 \u003d 10) we write zero, 1 goes to the next digit and it will be 19. We just cannot write 19 in the answer, since it should be clear that we rounded up to tenths - the figure in the category of tenths should be. Therefore, the answer is: 19.0.

Round to hundredths:

11) 2, 045; 12) 32,093; 13) 0, 7689; 14) 543, 008; 15) 67, 382.

Decision. We underline the number in the hundredth place and, depending on which digit is after the underlined one, leave the underlined number unchanged (if it is followed by 0, 1, 2, 3 or 4) or increase the underlined number by 1 (if it is followed by 5, 6, 7, 8 or 9).

11) 2, 0 4 5≈2,05;

12) 32,0 9 3≈32,09;

13) 0, 7 6 89≈0,77;

14) 543, 0 0 8≈543,01;

15) 67, 3 8 2≈67,38.

Important: the last digit in the answer should be the digit in the digit to which you rounded.

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How to round a number to an integer

Applying the rounding rule, consider concrete examples how to round a number to an integer.

Rule for rounding a number to an integer

To round a number to an integer (or round a number to units), you must discard the comma and all numbers after the decimal point.

If the first of the discarded digits is 0, 1, 2, 3, or 4, then the number will not change.

If the first of the discarded digits is 5, 6, 7, 8, or 9, the previous digit must be increased by one.

Round a number to an integer:

To round a number to an integer, we discard the comma and all the numbers after it. Since the first discarded digit is 2, the previous digit is not changed. They read: "eighty-six point twenty-four hundredths is approximately equal to eighty-six whole."

Rounding the number to an integer, we discard the comma and all the numbers following it. Since the first of the discarded digits is 8, the previous one is increased by one. They read: "Two hundred and seventy-four point eight hundred and thirty-nine thousandths is approximately equal to two hundred and seventy-five whole."

When rounding a number to an integer, we discard the comma and all the numbers behind it. Since the first of the discarded digits is 5, we increase the previous one by one. They read: "Zero point fifty-two hundredths is approximately equal to one whole."

We discard the comma and all the numbers after it. The first of the discarded digits is 3, so we do not change the previous digit. They read: "Zero point three hundred ninety-seven thousandths is approximately equal to zero point."

The first of the discarded digits is 7, which means that we increase the digit in front of it by one. They read: "Thirty-nine point seven hundred and four thousandths is approximately equal to forty point." And a couple more examples for rounding a number to integers:

27 Comments

Incorrect theory about if the number 46.5 is not 47 but 46, this is also called banking rounding to the nearest even rounded if after the decimal point 5 and there is no number after it

Dear ShS! Perhaps (?), In banks, rounding occurs according to other rules. I don't know, I don't work in a bank. This site is about the rules that apply in mathematics.

how to round the number 6.9?

To round a number to an integer, you must discard all numbers after the decimal point. We discard 9, so the previous number should be increased by one. So 6.9 is approximately equal to seven integers.

In fact, the figure really does not increase if after the decimal point 5 in any financial institution

Um. In this case, financial institutions in matters of rounding are not guided by the laws of mathematics, but by their own considerations.

Please tell me how to round 46.466667. confused

If you want to round a number to an integer, then you must discard all the digits after the decimal point. The first of the discarded digits is 4, so we do not change the previous digit:

Dear Svetlana Ivanovna, You are not familiar with the rules of mathematics.

Rule. If the digit 5 is discarded, and there are no significant figures behind it, then rounding is performed to the nearest even number, i.e. the last digit stored is left unchanged if it is even, and amplifies if it is odd.

And Accordingly: Rounding the number 0.0465 to the third decimal place, we write 0.046. We do not make amplifications, since the last saved digit 6 is even. The number 0.046 is as close to the given value as 0.047.

Dear guest! Let it be known to you, in mathematics for rounding numbers there are various ways rounding. At school, they study one of them, which consists in discarding the lower digits of the number. I am glad for you that you know another way, but it would be nice not to forget school knowledge.

Thank you very much! It was necessary to round 349.92. It turns out 350. Thanks for the rule?

how to round 5499.8 correctly?

If we are talking about rounding to an integer, then discard all the numbers after the decimal point. The discarded figure is 8, therefore, we increase the previous one by one. So 5499.8 is approximately equal to 5500 integers.

Good day!
But this question arose seyas:
There are three numbers: 60.56% 11.73% and 27.71% How to round up to whole numbers? That in the sum that 100 remained. If you just round up, then 61+12+28=101 There is a problem. (If, as you wrote, according to the "banking" method - in this case it will work, but in the case, for example, 60.5% and 39.5%, something will fall again - we will lose 1%). How to be?

O! the method from "guest 02.07.2015 12:11" helped
Thanks to"

I don't know, they taught me this in school:
1.5 => 1
1.6 => 2
1.51 => 2
1.51 => 1.6

Maybe that's how you were taught.

0, 855 to hundredths please help

0, 855≈0.86 (discarded 5, increase the previous figure by 1).

Round 2.465 to whole number

2.465≈2 (the first discarded digit is 4. Therefore, we leave the previous one unchanged).

How to round 2.4456 to an integer?

2.4456 ≈ 2 (since the first discarded digit is 4, we leave the previous digit unchanged).

Based on the rounding rules: 1.45=1.5=2, therefore 1.45=2. 1,(4)5 = 2. Is it true?

No. If you want to round 1.45 to an integer, discard the first digit after the decimal point. Since it's 4, we don't change the previous digit. Thus, 1.45≈1.