How to round up to integers after 5. How to round numbers up and down with Excel functions

Methods

AT different areas may apply various methods rounding. In all these methods, the "extra" signs are set to zero (discarded), and the sign preceding them is corrected according to some rule.

Rounding to nearest integer(English) rounding) - the most commonly used rounding, in which the number is rounded up to an integer, the modulus of the difference with which this number has a minimum. In general, when a number in the decimal system is rounded up to the Nth decimal place, the rule can be formulated as follows:
- if N+1 character< 5 , then the Nth sign is retained, and N+1 and all subsequent ones are set to zero;
- if N+1 characters ≥ 5, then the N-th sign is increased by one, and N + 1 and all subsequent ones are set to zero;
For example: 11.9 → 12; -0.9 → -1; −1,1 → −1; 2.5 → 3.
Rounding down modulo(rounding towards zero, integer Eng. fix, truncate, integer) is the most “simple” rounding, since after zeroing the “extra” signs, the previous sign is retained. For example, 11.9 → 11; −0.9 → 0; −1,1 → −1).
Rounding Up(round to +∞, round up, eng. ceiling) - if the nullable signs are not equal to zero, the preceding sign is increased by one if the number is positive, or kept if the number is negative. In economic jargon - rounding in favor of the seller, creditor(of the person receiving the money). In particular, 2.6 → 3, −2.6 → −2.
Rounding Down(round to −∞, round down, engl. floor) - if the nullable signs are not equal to zero, the preceding sign is retained if the number is positive, or incremented by one if the number is negative. In economic jargon - rounding in favor of the buyer, debtor(the person giving the money). Here 2.6 → 2, −2.6 → −3.
Rounding up modulo(round towards infinity, round away from zero) is a relatively rarely used form of rounding. If the nullable characters are not equal to zero, the preceding character is incremented by one.

Rounding options 0.5 to nearest integer

A separate description is required by the rounding rules for the special case when (N+1)th digit = 5 and subsequent digits are zero. If in all other cases, rounding to the nearest integer provides a smaller rounding error, then this particular case is characterized by the fact that for a single rounding it is formally indifferent whether to make it “up” or “down” - in both cases, an error of exactly 1/2 of the least significant digit is introduced . There are the following variants of the rounding rule to the nearest integer for this case:

Mathematical rounding- rounding is always up (the previous digit is always increased by one).
Bank rounding(English) banker's rounding) - rounding for this case occurs to the nearest even number, i.e. 2.5 → 2, 3.5 → 4.
Random rounding- rounding up or down randomly, but with equal probability (can be used in statistics).
Alternate rounding- Rounding occurs up or down alternately.

In all cases, when the (N + 1)th sign is not equal to 5 or subsequent signs are not equal to zero, rounding occurs according to the usual rules: 2.49 → 2; 2.51 → 3.

Mathematical rounding just formally corresponds to general rule rounding (see above). Its disadvantage is that when rounding a large number of values, accumulation can occur. rounding errors. Typical example: rounding to whole rubles of monetary amounts. So, if in the register of 10,000 lines there are 100 lines with amounts containing the value of 50 in terms of kopecks (and this is a very realistic estimate), then when all such lines are rounded “up”, the sum of the “total” according to the rounded register will be 50 rubles more than the exact .

The other three options are just invented in order to reduce the total error of the sum during rounding. a large number values. Rounding "to the nearest even" assumes that with a large number of rounded values that have 0.5 in the rounded remainder, on average, half will be to the left and half to the right of the nearest even, thus rounding errors will cancel each other out. Strictly speaking, this assumption is true only when the set of numbers being rounded has the properties of a random series, which is usually true in accounting applications where we are talking about prices, amounts in accounts, and so on. If the assumption is violated, then rounding “to even” can lead to systematic errors. For such cases, the following two methods work best.

The last two rounding options ensure that approximately half of the special values are rounded one way and half the other. But the implementation of such methods in practice requires additional efforts to organize the computational process.

Applications

Rounding is used to work with numbers within the number of digits that corresponds to the actual accuracy of the calculation parameters (if these values are real values measured in one way or another), the realistically achievable calculation accuracy, or the desired accuracy of the result. In the past, the rounding of intermediate values and the result was of practical importance (because when calculating on paper or using primitive devices such as the abacus, taking into account extra decimal places can seriously increase the amount of work). Now it remains an element of scientific and engineering culture. In accounting applications, in addition, the use of rounding, including intermediate ones, may be required to protect against computational errors associated with the finite bit capacity of computing devices.

Using rounding when working with numbers of limited precision

Real physical quantities are always measured with some finite accuracy, which depends on the instruments and methods of measurement and is estimated by the maximum relative or absolute deviation of the unknown actual value from the measured one, which in decimal representation of the value corresponds either to a certain number of significant digits, or to a certain position in the notation of a number, all the numbers after (to the right) of which are insignificant (they lie within the measurement error). The measured parameters themselves are recorded with such a number of characters that all figures are reliable, perhaps the last one is doubtful. The error in mathematical operations with numbers of limited precision is preserved and changes according to known mathematical laws, so when intermediate values and results with a large number of digits appear in further calculations, only a part of these digits are significant. The remaining figures, being present in the values, do not actually reflect any physical reality and only take time for calculations. As a result, intermediate values and results in calculations with limited accuracy are rounded to the number of decimal places that reflects the actual accuracy of the values obtained. In practice, it is usually recommended to store one more digit in intermediate values for long "chained" manual calculations. When using a computer, intermediate roundings in scientific and technical applications most often lose their meaning, and only the result is rounded.

So, for example, if a force of 5815 gf is given with an accuracy of a gram of force and a shoulder length of 1.4 m with an accuracy of a centimeter, then the moment of force in kgf according to the formula, in the case of a formal calculation with all signs, will be equal to: 5.815 kgf 1.4 m = 8.141 kgf m. However, if we take into account the measurement error, then we get that the limiting relative error of the first value is 1/5815 ≈ 1,7 10 −4 , second - 1/140 ≈ 7,1 10 −3 , the relative error of the result according to the error rule of the multiplication operation (when multiplying approximate values, the relative errors add up) will be 7,3 10 −3 , which corresponds to the maximum absolute error of the result ±0.059 kgf m! That is, in reality, taking into account the error, the result can be from 8.082 to 8.200 kgf m, thus, in the calculated value of 8.141 kgf m, only the first digit is completely reliable, even the second is already doubtful! It will be correct to round the calculation result to the first doubtful figure, that is, to tenths: 8.1 kgf m, or, if necessary, a more accurate indication of the margin of error, present it in a form rounded to one or two decimal places with an indication of the error: 8.14 ± 0.06 kgf m.

Empirical rules of arithmetic with rounding

In those cases where there is no need to accurately take into account computational errors, but only an approximate estimate of the number of exact numbers as a result of the calculation by the formula is required, you can use the set simple rules rounded calculations :

All raw values are rounded to the actual measurement accuracy and recorded with the appropriate number of significant digits, so that in decimal notation all figures were reliable (it is allowed that the last figure is doubtful). If necessary, the values are recorded with significant right zeros so that the actual number of reliable characters is indicated in the record (for example, if the length of 1 m is actually measured to the nearest centimeter, “1.00 m” is written so that it can be seen that two characters are reliable in the record after the decimal point), or the accuracy is explicitly indicated (for example, 2500 ± 5 m - here only tens are reliable, and should be rounded up to them).
Intermediate values are rounded off with one "spare" digit.
When adding and subtracting, the result is rounded to the last decimal place of the least accurate of the parameters (for example, when calculating a value of 1.00 m + 1.5 m + 0.075 m, the result is rounded to tenths of a meter, that is, to 2.6 m). At the same time, it is recommended to perform calculations in such an order as to avoid subtracting close numbers and to perform operations on numbers, if possible, in ascending order of their modules.
When multiplying and dividing, the result is rounded up to the smallest number significant digits that the parameters have (for example, when calculating the speed uniform motion body at a distance of 2.5 10 2 m, for 600 s the result should be rounded up to 4.2 m / s, since it is two digits that have a distance, and time has three, assuming that all the digits in the entry are significant).
When calculating the function value f(x) it is required to estimate the value of the modulus of the derivative of this function in the vicinity of the calculation point. If a (|f"(x)| ≤ 1), then the result of the function is exact to the same decimal place as the argument. Otherwise, the result contains fewer exact decimal places by the amount log 10 (|f"(x)|), rounded to the nearest integer.

Despite the non-strictness, the above rules work quite well in practice, in particular, because of the rather high probability of mutual cancellation of errors, which is usually not taken into account when errors are accurately taken into account.

Mistakes

Quite often there are abuses of non-round numbers. For example:

Write down numbers that have low accuracy, in unrounded form. In statistics: if 4 people out of 17 answered “yes”, then they write “23.5%” (while “24%” is correct).
Pointer users sometimes think like this: “the pointer stopped between 5.5 and 6 closer to 6, let it be 5.8” - this is also prohibited (the graduation of the device usually corresponds to its actual accuracy). In this case, you need to say "5.5" or "6".

Notes

Literature

Henry S. Warren, Jr. Chapter 3// Algorithmic tricks for programmers = Hacker's Delight. - M .: Williams, 2007. - S. 288. - ISBN 0-201-91465-4

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, which look like 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 converting a number to comfortable view 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.

Fractional numbers in Excel spreadsheets can be displayed to varying degrees. accuracy:

most simple method - on the tab " home» press the buttons « Increase bit depth" or " Decrease bit depth»;
click right click by cell, in the drop-down menu, select " Cell Format...”, then the tab “ Number", select the format" Numerical”, determine how many decimal places there will be after the decimal point (2 decimal places are suggested by default);
click the cell, on the tab " home» choose « Numerical", or go to " Other number formats...” and configure there.

Here's what the fraction 0.129 looks like if you change the number of decimal places in the cell format:

Please note that A1,A2,A3 have the same meaning, only the form of representation changes. In further calculations, not the value visible on the screen will be used, but original. For a novice spreadsheet user, this can be a little confusing. To really change the value, you need to use special functions, there are several of them in Excel.

Rounding formula

One of the commonly used rounding functions is ROUND. It works according to standard mathematical rules. Select a cell, click the " Insert function”, category “ Mathematical", we find ROUND

We define the arguments, there are two of them - herself fraction and amount discharges. We click " OK' and see what happens.

For example, the expression =ROUND(0.129,1) will give a result of 0.1. The zero number of digits allows you to get rid of the fractional part. Choosing a negative number of digits allows you to round the integer part to tens, hundreds, and so on. For example, the expression =ROUND(5,129,-1) will give 10.

Round up or down

Excel provides other tools that allow you to work with decimals. One of them - ROUNDUP, gives the closest number, more modulo. For example, the expression =ROUNDUP(-10,2,0) will give -11. The number of digits here is 0, which means we get an integer value. nearest integer, greater in modulus, - just -11. Usage example:

ROUNDDOWN similar to the previous function, but returns the closest value that is smaller in absolute value. The difference in the work of the above means can be seen from examples:

=ROUND(7,384,0)	7
=ROUNDUP(7,384,0)	8
=ROUNDDOWN(7,384,0)	7
=ROUND(7,384,1)	7,4
=ROUNDUP(7,384,1)	7,4
=ROUNDDOWN(7,384,1)	7,3

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:

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 observed.

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. AT this case the digit 8 will be enhanced to 9 , since the first digit to cut off is 6 , which 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 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, let's 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.

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 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 hundredths 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.

www.mathematics-repetition.com

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.