Rule for rounding digits after the decimal point. You searched for: round to tenths

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). In 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 that 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 zeros in decimals 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 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?

Turns out, most of people in the world are not in 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).

can lead great amount 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 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, given number cannot be used for counting specific subjects and 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 must be removed, the odd digit is increased by 1. But only on the condition that there is no after the "5" significant figures. 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.

Under rounding natural number understand replacing it with such a number closest in value, in which one or several last digits in its record are replaced by zeros.

Rounding rule:

To round a natural number, you need to select the digit in the number entry to which rounding is performed.

The number written in the selected digit:

does not change if the digit following it on the right is 0, 1, 2, 3 or 4;

All digits to the right of this bit are replaced by zeros.

Example: 14 3 ≈ 140 (rounded to the nearest tens);
56 71 ≈ 5700 (rounded to the nearest hundred).

If the digit to which rounding is performed contains the number 9 and it is necessary to increase it by one, then the digit 0 is written in this digit, and the digit in the adjacent high-order digit (on the left) is increased by 1.

Example: 79 6 ≈ 800 (rounded to tens);
9 70 ≈ 1000 (rounded to the nearest hundred).

Rounding decimals

To round up decimal, you need to select the digit in the number entry to which rounding is performed. The number written in this category:

increments by one if the next digit to the right is 5,6,7,8, or 9.

All digits to the right of this bit are replaced by zeros. If these zeros are in the fractional part of the number, then they are not written.

Example: 143,6 4 ≈ 143.6 (rounded to tenths);
5,68 7 ≈ 5.69 (rounded to hundredths);
27 .945 ≈ 28 (rounded to the nearest integer).

If the digit to which rounding is performed contains the number 9 and it is necessary to increase it by one, then the digit 0 is written in this digit, and the figure in the previous digit (on the left) is increased by 1.

Example: 8 9, 6 ≈ 90 (rounded to tens);
0,09 7 ≈ 0.10 (rounded to hundredths).

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Rounding numbers

1) Rules for rounding natural numbers. Natural numbers are rounded to units of a certain digit. To round a natural number to units of a certain digit means to establish how many units of this digit are contained in a given number. For example, we want to round the number 237456 to the nearest thousand. This means to find out how many thousands there are in this number. Obviously, it has 237 thousand. How did we know? To do this, we all the digits of a given number up to the thousands place, i.e. hundreds, tens and ones, replaced with zeros and got the number 237000, which can be written in short like this: 237 thousand. But you can, knowing that 1000=10 3, write this rounded number like this: 237*10 3 .

So, 237456? 237 thousand or 237 456? 237*10 3 .

Please note that here we did not put the usual equal sign, but approximate equal sign (?).

Why such a sign? Yes, because the numbers 237,456 and 237 thousand are not equal, the second number is somewhat less than the first, namely, less than 456, therefore, replacing the number 237,456 with the number 237 thousand, we thereby make an error equal to 456, which means that the numbers 237,456 and 237,000 are only approximately equal. Therefore, the sign of approximate equality is put. Note that the error in rounding the number 237,456 to thousands was 456 units, which is less than half of one thousand. Therefore, if we need to round the number 237 873 to thousands, then it is more reasonable to take 237 thousand as the rounded value of the number 237 873, then let's make an error equal to 873, which is more than half a thousand, i.e. 500. If the rounded value is 238 thousand, then the error will be only 127, which is much less than half a thousand. From these examples, we can deduce the following general rule rounding natural numbers to units of a certain digit: replace all digits to the right of this digit with zeros. If the first digit on the left of those replaced by zeros is less than 5, then the rounding is completed and the resulting rounded number can be written in an abbreviated form. If it is equal to or greater than 5, then the digit of the digit to which rounding was performed is replaced by a larger one.

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Rounding natural numbers.

We often use rounding in Everyday life. If the distance from home to school is 503 meters. We can say, by rounding up the value, that the distance from home to school is 500 meters. That is, we have brought the number 503 closer to the more easily perceived number 500. For example, a loaf of bread weighs 498 grams, then by rounding the result we can say that a loaf of bread weighs 500 grams.

rounding- this is the approximation of a number to a “lighter” number for human perception.

The result of rounding is approximate number. Rounding is indicated by the symbol ≈, such a symbol reads “approximately equal”.

You can write 503≈500 or 498≈500.

Such an entry is read as “five hundred three is approximately equal to five hundred” or “four hundred ninety-eight is approximately equal to five hundred”.

Let's take another example:

4 4 71≈4000 4 5 71≈5000

4 3 71≈4000 4 6 71≈5000

4 2 71≈4000 4 7 71≈5000

4 1 71≈4000 4 8 71≈5000

4 0 71≈4000 4 9 71≈5000

In this example, numbers have been rounded to the thousands place. If we look at the rounding pattern, we will see that in one case the numbers are rounded down, and in the other - up. After rounding, all other numbers after the thousands place were replaced by zeros.

Number rounding rules:

1) If the figure to be rounded is equal to 0, 1, 2, 3, 4, then the digit of the digit to which the rounding is going does not change, and the rest of the numbers are replaced by zeros.

2) If the figure to be rounded is equal to 5, 6, 7, 8, 9, then the digit of the digit to which the rounding is going on becomes 1 more, and the remaining numbers are replaced by zeros.

1) Round to the tens place of 364.

The digit of tens in this example is the number 6. After the six there is the number 4. According to the rounding rule, the number 4 does not change the digit of the tens. We write zero instead of 4. We get:

2) Round to the hundreds place of 4781.

The hundreds digit in this example is the number 7. After the seven is the number 8, which affects whether the hundreds digit changes or not. According to the rounding rule, the number 8 increases the hundreds place by 1, and the rest of the numbers are replaced by zeros. We get:

3) Round to the thousands place of 215936.

The thousands place in this example is the number 5. After the five is the number 9, which affects whether the thousands place changes or not. According to the rounding rule, the number 9 increases the thousands place by 1, and the remaining numbers are replaced by zeros. We get:

21 5 9 36≈21 6 000

4) Round to the tens of thousands of 1,302,894.

The thousand digit in this example is the number 0. After zero, there is the number 2, which affects whether the tens of thousands digit changes or not. According to the rounding rule, the number 2 does not change the digit of tens of thousands, we replace this digit and all digits of the lower digits with zero. We get:

13 0 2 894≈13 0 0000

If exact value number is unimportant, then the value of the number is rounded off and you can perform computational operations with approximate values. The result of the calculation is called estimation of the result of actions.

For example: 598⋅23≈600⋅20≈12000 is comparable to 598⋅23=13754

An estimate of the result of actions is used in order to quickly calculate the answer.

Examples for assignments on the topic rounding:

Example #1:
Determine to what digit rounding is done:
a) 3457987≈3500000 b) 4573426≈4573000 c) 16784≈17000
Let's remember what are the digits on the number 3457987.

7 - unit digit,

8 - tens place,

9 - hundreds place,

7 - thousands place,

5 - digit of tens of thousands,

4 - hundreds of thousands digit,
3 is the digit of millions.
Answer: a) 3 4 57 987≈3 5 00 000 digit of hundreds of thousands b) 4 57 3 426 ≈ 4 57 3 000 digit of thousands c) 1 6 7 841 ≈ 1 7 0 000 digit of tens of thousands.

Example #2:
Round the number to 5,999,994 places: a) tens b) hundreds c) millions.
Answer: a) 5 999 99 4 ≈5 999 990 b) 5 999 9 9 4 ≈6 000 000 994≈6,000,000.

Rules for rounding natural numbers

Rules for rounding natural numbers.
Rounding a number up to some digit.

From time to time, a population census is conducted in the country. Every day people are born, die, change their place of residence, so the number of inhabitants is constantly changing. Let's say that there are 34,489 inhabitants in one city. Accordingly, when people move in this number, the numbers of the digits of units, tens and even hundreds will change. Such numbers are replaced with zeros, and we get a simpler number. It can be said that he lives in the city approximately 34,000 inhabitants.

The number 34 489 was rounded up to 3 thousand 4 000.
If we want to round some number, then we apply the rule:
45|245 - the line shows to what digit we want to round.

If the first digit following the digit to which the number is rounded (to the right of the bar) is 5, 6, 7, 8, 9, then the last remaining digit is increased by 1, and the rest of the digits after the dash are replaced by zeros. In other cases, the last remaining digit is not changed.

The given number and the number obtained by rounding it approximately equal.This is written with the sign » » «.
45|245 » 45,000, since the digit following the thousands place is 2.
124 7 | 89 » 124 800, since the digit following the hundreds place is 8.

Round the numbers 12,344; 12,343; 12,342; 12 340; 12,341 to tens.
.

Rounding of natural numbers is used when calculating the price. Subtractions are made orally, an estimate of the result is made. For instance:
358 56 = 20,048

For simplified multiplication, round each number:
358 » 400 and 56 » 60 400 x 60 = 24 000

It can be seen that this answer is approximately equal to the first answer.

1. Give examples where you can use rounding numbers..
.
.

2. Explain to what digit the numbers are rounded. The first column has been rounded to the nearest tens. The second column has been rounded to the nearest thousand.

6789 » 6800 . 12 897 » 10 000 .
12 544 » 12 500 . 2 344 672 » 2 340 000 .
245 673 » 245 700 . 78 358 » 78 360 .
26 577 » 30 000 . 34 057 123 » 34 100 000 .

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. The names of the digits in the digits of a natural number can be recalled 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 the number 5, 6, 7, 8 or 9 is to the right of the underlined digit, 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 drawback.

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.

The Microsoft Excel program also works with numerical data. When performing division or working with fractional numbers, the program performs rounding. This is primarily due to the fact that absolutely accurate fractional numbers are rarely needed, but it is not very convenient to operate with a cumbersome expression with several decimal places. In addition, there are numbers that, in principle, do not exactly round off. But, at the same time, insufficiently accurate rounding can lead to gross errors in situations where precision is required. Fortunately, in Microsoft Excel, it is possible for users to set how numbers will be rounded.

All numbers that Microsoft Excel works with are divided into exact and approximate. Numbers up to 15 digits are stored in memory, and are displayed up to the digit that the user himself indicates. But, at the same time, all calculations are performed according to the data stored in memory, and not displayed on the monitor.

With the rounding operation, Microsoft Excel discards a number of decimal places. Excel uses the conventional rounding method where a number less than 5 is rounded down, and a number greater than or equal to 5 is rounded up.

Rounding with Ribbon Buttons

by the most in a simple way to change the rounding of a number is to select a cell or group of cells, and being in the "Home" tab, click on the button "Increase bit depth" or "Decrease bit depth" on the ribbon. Both buttons are located in the "Number" toolbox. In this case, only the displayed number will be rounded, but for calculations, if necessary, up to 15 digits of numbers will be involved.

When you click on the "Increase bit depth" button, the number of entered decimal places is increased by one.

When you click on the "Decrease bit depth" button, the number of digits after the decimal point is reduced by one.

Rounding Through Cell Format

You can also set rounding using the cell format settings. To do this, you need to select a range of cells on the sheet, right-click, and select "Format Cells" from the menu that appears.

In the cell format settings window that opens, go to the "Number" tab. If the data format is not numeric, then you need to select the numeric format, otherwise you will not be able to adjust the rounding. In the central part of the window near the inscription "Number of decimal places" simply indicate the number of characters that we want to see when rounding. After that, click on the "OK" button.

Set calculation accuracy

If in previous cases, the set parameters only affected the external display of data, and more accurate indicators (up to 15 digits) were used in the calculations, now we will tell you how to change the very accuracy of the calculations.

The Excel Options window opens. In this window, go to the "Advanced" subsection. We are looking for a block of settings called "When recalculating this book." The settings in this section apply not to a single sheet, but to the entire book as a whole, that is, to the entire file. Put a check next to the "Set accuracy as on screen" option. Click on the "OK" button located in the lower left corner of the window.

Now, when calculating the data, the displayed value of the number on the screen will be taken into account, and not the one that is stored in Excel's memory. Setting the displayed number can be done in any of the two ways that we talked about above.

Application of functions

If you want to change the rounding value when calculating relative to one or more cells, but do not want to reduce the accuracy of calculations for the document as a whole, then in this case, it is best to use the opportunities provided by the ROUND function and its various variations, as well as some other features.

Among the main functions that regulate rounding, the following should be highlighted:

ROUND - rounds up to specified date decimal places, according to generally accepted rounding rules;
ROUNDUP - rounds up to the nearest number up by the modulo;
ROUNDDOWN - rounds down to the nearest number in modulo;
ROUND - rounds a number with a given precision;
ROUNDUP - rounds a number with a given precision up in modulus;
ROUNDDOWN - rounds the number down modulo with the specified precision;
OTBR - rounds the data to an integer;
EVEN - rounds data to the nearest even number;
ODD - rounds the data to the nearest odd number.

For the ROUND, ROUNDUP, and ROUNDDOWN functions, the following input format is: “Function name (number;number_digits). That is, if you, for example, want to round the number 2.56896 to three digits, then use the ROUND(2.56896; 3) function. The output is 2.569.

For the ROUND, ROUNDUP, and ROUNDUP functions, the following rounding formula is used: "Function name (number, precision)". For example, to round the number 11 to the nearest multiple of 2, enter the function ROUND(11;2). The output is 12.

The FIND, EVEN, and ODD functions use the following format: "Function name (number)". In order to round the number 17 to the nearest even number, use the EVEN(17) function. We get the number 18.

A function can be entered both in a cell and in a line of functions, having previously selected the cell in which it will be located. Each function must be preceded by an "=" sign.

There is a slightly different way to introduce rounding functions. It is especially useful when you have a table with values that need to be converted to rounded numbers in a separate column.

To do this, go to the Formulas tab. Click on the "Math" button. Next, in the list that opens, select the desired function, for example, ROUND.

After that, the function arguments window opens. In the "Number" field, you can enter a number manually, but if we want to automatically round the data of the entire table, then click on the button to the right of the data entry window.

The function arguments window is minimized. Now we need to click on the topmost cell of the column whose data we are going to round. After the value is entered in the window, click on the button to the right of this value.

The function arguments window opens again. In the field "Number of digits" we write the bit depth to which we need to reduce fractions. After that, click on the “OK” button.

As you can see, the number has been rounded. In order to round all other data of the desired column in the same way, hover over the lower right corner of the cell with the rounded value, click on the left mouse button, and drag it down to the end of the table.

After that, all values in the desired column will be rounded.

As you can see, there are two main ways to round the visible display of a number: using the button on the ribbon, and by changing the cell format options. In addition, you can change the rounding of actually calculated data. This can also be done in two ways: by changing the settings of the book as a whole, or by using special functions. The choice of a specific method depends on whether you are going to apply this kind of rounding to all data in the file, or only to a certain range of cells.

Let's look at examples of how to round up to tenths of a number using the rounding rules.

Rule for rounding numbers to tenths.

To round a decimal to tenths, you must leave only one digit after the decimal point, and discard all other digits following it.

If the first of the discarded digits is 0, 1, 2, 3 or 4, then the previous digit is not changed.

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

Examples.

Round to tenths:

To round a number to tenths, leave the first digit after the decimal point, and discard the rest. Since the first discarded digit is 5, we increase the previous digit by one. They read: "Twenty-three point seventy-five hundredths is approximately equal to twenty-three point eight."

To round this number to tenths, leave only the first digit after the decimal point, discard the rest. The first discarded digit is 1, so the previous digit is not changed. They read: "Three hundred and forty-eight point thirty-one hundredth is approximately equal to three hundred and forty-one point three."

Rounding to tenths, we leave one digit after the decimal point, and discard the rest. The first of the discarded digits is 6, which means that we increase the previous one by one. They read: "Forty-nine point, nine hundred and sixty-two thousandths is approximately equal to fifty point, zero tenths."

We round up to tenths, so after the comma we leave only the first of the digits, the rest are discarded. The first of the discarded digits is 4, which means we leave the previous digit unchanged. They read: "Seven point twenty-eight thousandths is approximately equal to seven point zero tenths."

To round to tenths, this number leaves one digit after the decimal point, and discard all following after it. Since the first discarded digit is 7, therefore, we add one to the previous one. They read: "Fifty-six point eight thousand seven hundred and six ten-thousandths is approximately equal to fifty-six point nine-tenths."

And a couple more examples for rounding to tenths: