Rounding methods

V different areas can be applied different methods rounding off. In all these methods, the "extra" signs are set to zero (discarded), and the preceding sign is corrected according to some rule.

• Rounding to the nearest integer(eng. round) is the most commonly used rounding. Number in decimal system round up to the Nth decimal place depending on N + 1 decimal places:
  • if N + 1 digit< 5 , then the N-th sign is preserved, and N + 1 and all subsequent ones are set to zero;
  • if N + 1 digit ≥ 5, then the N-th sign is increased by one, and N + 1 and all subsequent ones are zeroed.
  For example: 11.9 → 12; −0.9 → −1; −1.1 → −1; 2.5 → 3.
• Round down in absolute value(rounding towards zero, whole eng. fix, truncate, integer) is the "simplest" rounding, because after zeroing out the "extra" characters, the previous character is retained. For example, 11.9 → 11; −0.9 → 0; −1,1 → −1).
• Round up(rounding to + ∞, rounding up, eng. ceil) - 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(the person receiving the money). In particular, 2.6 → 3, −2.6 → −2.
• Round down(rounding to −∞, rounding down, eng. floor) - if the nullable signs are not equal to zero, the preceding sign is retained if the number is positive, or increased 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(rounding towards infinity, rounding away from zero) is a relatively rarely used form of rounding, if the nullable characters are not equal to zero, the preceding character is increased by one.

Rounding options to nearest integer

In these options, the rule has been changed for the case (N + 1) th sign = 5 and subsequent signs are equal to zero.

• Banking rounding(eng. banker "s rounding) - rounding for this case occurs to the nearest even. This eliminates systematic rounding error when summing a large number of numbers. That is, 2.5 → 2, 3.5 → 4.
• Random rounding- rounding down or big side in random order, but with equal probability (can be used in statistics).
• Alternating rounding- rounding up or down one by one.

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

Using rounding

Rounding is used for several purposes:

• Convenience of working with round numbers. In case the exact meaning of the number is not important, it is easier to use round numbers.
• an indication of the accuracy of the measurement.

"Anti-rounding"

Non-circular numbers are abused quite often. For instance:

• The numbers that actually have low accuracy are recorded in an unrounded form.
  • In statistics: if 4 people out of 17 answered “yes”, then they write “23.5%” (while “24%” is correct). In particular, in the case statistical research it is considered bad form if the number of respondents is such that “round” response rates are formed.
  • Users of dial gauges sometimes think like this: “the arrow stopped between 5 and 6 closer to 6, let it be 5.7” - this is also prohibited (the graduation of the device always corresponds to its real accuracy). In this case, you should say "5.5" or "6".
• Stores often set “non-round” prices to create the impression of a lower price for the buyer (for example, instead of 200 rubles, they write 199 rubles).

Links

• Processing observations
• Rounding errors

Literature

• Henry S. Warren, Jr. Chapter 3. Rounding to a power of 2// Algorithmic tricks for programmers = Hacker "s Delight. - M .:" Williams ", 2007. - P. 288. - ISBN 0-201-91465-4

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In approximate calculations, it is often necessary to round off some numbers, both approximate and exact, that is, remove one or more final digits. There are some rules to follow to ensure that an individual rounded number is as close as possible to the number being rounded.

If the first of the separated digits is greater than the number 5, then the last of the remaining digits is amplified, in other words, it is increased by one. Strengthening is also assumed when the first of the removed digits is 5, and after it there is one or some significant digits.

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

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

If the first of the cut-off digits is less than 5, then amplification is not performed.

The number 46.48 is rounded off as - 46. 46 is closer to the number to be rounded 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 digit left remains unchanged if it is even, and is amplified if it is odd.

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

The number 0.935 is rounded off as - 0.94. The last digit 3 to be left is amplified as it is odd.

Rounding numbers

Numbers are rounded up when full precision is unnecessary or impossible.

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

Natural numbers are rounded to tens, hundreds, thousands, etc. Digit names in digits natural number you can recall natural numbers in the topic.

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

If the number is rounded to tens, then we replace the digit in the one place with zeros.

If the number is rounded up to hundreds, then the digit zero must be in both the ones and tens places.

The number obtained by rounding off is called an approximate value. this number.

Record the rounding result after the special sign "≈". This sign reads “approximately equal”.

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

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

Let us explain with an example. Let's round up 57,861 to thousands. Let's execute the first two points of the rounding rules.

After the underlined number there is a number 8, which means that we add 1 to the number of the thousand place (we have 7), and replace all the numbers separated by a vertical line with zeros.

Now let's round 756,485 to hundreds.

Let's round 364 to tens.

3 6 | 4 ≈ 360 - it costs 4 in the ones place, so we leave 6 in the tens place unchanged.

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

Number 360 - approximate downside value, and the number 370 is an approximate excess value.

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

Rounded results are often written without zeros, adding the abbreviations "thousand" (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 accurate calculation, let's make an estimate of the answer, rounding the multipliers 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 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 objects in other situations. Then the given number should be reduced to a certain place, for example, to an integer or to a number with a decimal place. If we bring 3.3333333333… ..3 to an integer, then we get 3, and converting 3.3333333333… ..3 to a number with a decimal place, we get 3.3.

Rounding rules

What is rounding? This is to drop a few digits that are the last in the exact number row. So, following our example, we dropped all the last digits to get an integer (3) and dropped the digits, leaving only the tens (3.3) places. The number can be rounded to hundredths and thousandths, ten thousandths and other numbers. It all depends on how accurate the number is to get. For example, when making medical supplies, the amount of each of the ingredients of the medicine is taken with the greatest accuracy, since even a thousandth of a gram can be fatal. If it is necessary to calculate what the performance of students in school is, then most often a number with a decimal or with a hundredth place is used.

Consider another example that uses rounding rules. For example, there is a number 3.583333, which needs to 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, because after the “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 digit stored remains unchanged. Such rules for rounding numbers apply regardless of whether to an integer or to tens, hundredths, etc. you need to round off the number.

In most cases, when you need to round a number with the last digit "5", this process is not performed correctly. But there is also such a rounding rule that applies to just such cases. Let's look at an example. 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 up 3.35, the result would be 3.4. Since, in accordance with the rounding rules, if there is an odd digit before "5" that must be removed, the odd digit is increased by 1. But only on the condition that there are no significant digits after "5". In many cases, simplified rules can be applied, according to which, if there are digit values ​​from 0 to 4 behind the last stored digit, the stored digit does not change. If there are other digits, the last digit is increased by 1.

5.5.7. Rounding numbers

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

Examples.

Round up to integers:

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

Solution. We underline the number in the category of units (whole) and look at the number behind it. If this is the number 0, 1, 2, 3 or 4, then we leave the underlined number unchanged, and discard all the numbers after it. 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.

Solution. We underline the number in the tenth place, and then we act according to the rule: we discard everything after the underlined number. If the underlined digit was followed by the digit 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 = 10) write zero, 1 goes to the next digit and it will be 19. It's just that we can't write 19 in the answer, since it should be clear that we were rounding to tenths - the number in the tenth place 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.

Solution. We underline the digit in the hundredth place and, depending on which digit is after the underlined one, leave the underlined digit unchanged (if it is followed by 0, 1, 2, 3 or 4) or increase the underlined digit 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: in the answer of the latter there should be a digit in the place to which you rounded.

www.mathematics-repetition.com

How to round a number to an integer

Applying the rule for rounding numbers, consider specific examples how to round a number to an integer.

The rule for rounding a number to an integer

To round a number to an integer (or round a number to one), you need to drop the comma and all numbers after the comma.

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 up a number to an integer:

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

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

When rounding a number to an integer, discard 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 points."

The first of the discarded digits is 7, which means that the digit in front of it is increased by one. They read: "Thirty-nine point seven hundred and four thousandths is approximately equal to forty points." 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 bank rounding to the nearest even, it is rounded if after the decimal point 5 and there is no number behind it

Dear ShS! Perhaps (?), In banks rounding takes place according to different rules. I don’t know, I don’t work in a bank. This site deals with the rules in force in mathematics.

how to round the number 6.9?

To round a number to an integer, discard all numbers after the decimal point. We discard 9, so the previous number should be increased by one. This means that 6.9 is approximately equal to seven points.

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

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

Tell me how to round 46.466667. Got confused

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

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

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

And accordingly: Rounding the number 0.0465 to the third decimal place, we write 0.046. We do not amplify, since the last stored digit 6 is even. The number 0.046 is as close to the given number as 0.047.

Dear Guest! Let it be known to you, in mathematics there are numbers for rounding different ways rounding off. At school, one of them is studied, which consists in discarding the lower digits of a 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 off 5499.8 correctly?

If we are talking about rounding to the nearest integer, then discard all digits after the decimal point. The discarded figure is 8, therefore, we increase the previous one by one. This means that 5499.8 is approximately 5500 integers.

Good day!
But this question arose seias:
There are three numbers: 60.56% 11.73% and 27.71% How to round up to whole values? So that a total of 100 remains. If you just round up, then 61 + 12 + 28 = 101 There is a discrepancy. (If, as they wrote, according to the "banking" method - in this case it will work, but in the case of, for example, 60.5% and 39.5%, it will turn out to be something else again - we will lose 1%). How to be?

O! helped by the method from "guest 07/02/2015 12:11"
Thanks to"

I don’t know I was taught at school like this:
1.5 => 1
1.6 => 2
1.51 => 2
1.51 => 1.6

Perhaps you were taught that way.

0, 855 to hundredths please help

0, 855≈0.86 (5 dropped, the previous figure is increased by 1).

Round 2,465 to an integer

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

How to round 2.4456 to the nearest integer?

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

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

No. If you want to round 1.45 to the nearest integer, discard the first decimal place. Since it is 4, we do not change the previous digit. Thus, 1.45≈1.

§ 4. Rounding of results

The processing of measurement results in laboratories is carried out on calculators and a PC, and it is simply amazing how magically long series of digits after the decimal point magically affects many students. “That's more accurate,” they say. However, it is easy to see, for example, that writing a = 2.8674523 ± 0.076 is meaningless. With an error of 0.076, the last five digits of the number mean absolutely nothing.

If we make a mistake in hundredths, then there is no faith in thousandths, let alone ten thousandths. A competent record of the result would be 2.87 ± 0.08. It is always necessary to make the necessary rounding so that there is no false impression that the results are more accurate than they really are.

Rounding rules

1. The measurement error is rounded to the first significant digit, always increasing by one.
   Examples:

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

2. The measurement results are rounded off with an accuracy "to an error", i.e. the last significant digit in the result must be in the same place as in the error.
   Examples:

   243.871 ± 0.026 ≈ 243.87 ± 0.03;
   243.871 ± 2.6 ≈ 244 ± 3;
   1053 ± 47 ≈ 1050 ± 50.

3. Rounding off the measurement result is achieved by simply dropping the digits if the first of the discarded digits is less than 5.
   Examples:

   8.337 (round to tenths) ≈ 8.3;
   833.438 (round to integers) ≈ 833;
   0.27375 (round to hundredths) ≈ 0.27.

4. If the first of the discarded digits is greater than or equal to 5 (followed by one or more digits other than zero), then the last of the remaining digits is increased by one.
   Examples:

   8.3351 (round to decimal places) ≈ 8.34;
   0.2510 (round to tenths) ≈ 0.3;
   271.515 (round to integers) ≈ 272.

5. If the discarded digit is 5, and there are no significant digits behind it (or there are only zeros), then the last left digit is increased by one when it is odd, and left unchanged when it is even.
   Examples:

   0.875 (round to the nearest hundredth) ≈ 0.88;
   0.5450 (round to hundredths) ≈ 0.54;
   275.500 (round to integers) ≈ 276;
   276.500 (round to integers) ≈ 276.

Note.

1. Significant is the correct digits of a number, except for the leading zeros. For example, 0.00807 - this number has three significant digits: 8, zero between 8 and 7 and 7; the first three zeros are insignificant.
   8.12 · 10 3 - this number contains 3 significant digits.
2. The 15.2 and 15,200 entries are different. Recording 15,200 means that hundredths and thousandths are correct. In the record 15.2 - whole and tenths are correct.
3. results physical experiments write down only in significant numbers. A comma is placed immediately after a nonzero digit, and the number is multiplied by ten to the appropriate power. Leading or trailing zeros are usually not written. For example, the numbers 0.00435 and 234000 are written like this: 4.35 x 10 -3 and 2.34 x 10 5. This notation simplifies calculations, especially in the case of formulas that are convenient for taking logarithms.

This CMEA standard establishes the rules for recording and rounding numbers expressed in decimal notation.

The rules for recording and rounding numbers established in this CMEA standard are intended for use in normative-technical, design and technological documentation.

This CMEA standard does not apply to the special rounding rules established in other CMEA standards.

1. RULES FOR RECORDING NUMBERS

1.1. Significant digits of a given number are all digits from the first to the left, not equal to zero, up to the last recorded digit to the right. In this case, the zeros following from the factor 10 n are not taken into account.

	1. Number 12.0	has three significant digits;
	2. Number 30	has two significant digits;
	3. Number 120 · 10 3	has three significant digits;
	4. Number 0.514 · 10	has three significant digits;
	5. Number 0.0056	has two significant digits.

1.2. When it is necessary to indicate that a number is exact, the word “exactly” must be indicated after the number, or the last significant digit is printed in bold

Example. In printed text:

1 kWh = 3,600,000 J (exact), or = 3,600,000 J

1.3. Records of approximate numbers should be distinguished by the number of significant digits.

Examples:

1. A distinction should be made between the numbers 2.4 and 2.40. The entry 2.4 means that only whole and tenth digits are correct; true meaning numbers can be for example 2.43 and 2.38. The record 2.40 means that the hundredths of the number are also correct; the true number can be 2.403 and 2.398, but not 2.421 or 2.382.

2. Record 382 means that all digits are correct; if the last digit cannot be vouched for, then the number should be written down 3.8 · 10 2.

3. If in the number 4720 only the first two digits are correct, it should be written 47 · 10 2 or 4.7 · 10 3.

1.4. The number for which the permissible deviation is indicated must have the last significant digit of the same order as the last significant digit of the deviation.

Examples:

1.5. It is advisable to write the numerical values ​​of the quantity and its errors (deviations) with the indication of the same unit of physical quantities.

Example. 80.555 ± 0.002 kg

1.6. The intervals between the numerical values ​​of the quantities should be recorded:

60 to 100 or 60 to 100

Over 100 to 120 or over 100 to 120

Over 120 to 150 or over 120 to 150.

1.7. Numerical values ​​of quantities should be indicated in standards with the same number of digits, which is necessary to ensure the required operational properties and product quality. The recording of numerical values ​​of quantities up to the first, second, third, etc. decimal places for different standard sizes, types of brands of products of the same name, as a rule, should be the same. For example, if the gradation of the thickness of the hot-rolled steel strip is 0.25 mm, then the entire range of strip thicknesses must be indicated with an accuracy of two decimal places.

Depending on the technical characteristics and purpose of the product, the number of decimal places for the numerical values ​​of the same parameter, size, indicator or norm may have several steps (groups) and should be the same only within this step (group).

2. RULES OF ROUND

2.1. Rounding of a number is the casting of significant digits from the right to a certain digit with a possible change in the digit of this digit.

Example. Rounding 132.48 to four significant digits is 132.5.

2.2. If the first of the discarded digits (counting from left to right) is less than 5, then the last stored digit does not change.

Example. Rounding 12.23 to three significant digits gives 12.2.

2.3. If the first of the discarded digits (counting from left to right) is 5, then the last stored digit is increased by one.

Example. Rounding 0.145 to two significant digits gives 0.15.

Note. In cases where the results of previous rounding should be taken into account, you should proceed as follows:

1) if the discarded digit was the result of the previous rounding up, then the last stored digit is saved;

Example. Rounding to one significant digit of 0.15 (obtained after rounding 0.149) gives 0.1.

2) if the discarded digit was the result of the previous rounding down, then the last remaining digit is increased by one (with transition, if necessary, to the next digits).

Example. Rounding 0.25 (resulting from the previous rounding of 0.252) gives 0.3.

2.4. If the first of the discarded digits (counting from left to right) is greater than 5, then the last stored digit is increased by one.

Example. Rounding 0.156 to two significant digits gives 0.16.

2.5. Rounding should be done immediately to the desired number of significant figures, not step by step.

Example. Rounding 565.46 to three significant digits directly on 565. Rounding in steps would result in:

565.46 in stage I - to 565.5,

and in the second stage - 566 (wrongly).

2.6. Whole numbers are rounded off using the same rules as fractional numbers.

Example. Rounding 12 456 to two significant digits gives 12 · 10 3.

Topic 01.693.04-75.

3. The CMEA standard was approved at the 41st meeting of the PKS.

4. Terms of the beginning of the application of the CMEA standard:

CMEA member countries	The term for the commencement of the application of the CMEA standard in contractual and legal relations on economic, scientific and technical cooperation	The date of commencement of the application of the CMEA standard in national economy
NRB	December 1979	December 1979
Hungarian People's Republic	December 1978	December 1978
GDR	December 1978	December 1978
Republic of Cuba
Mongolia
Poland
CPP
the USSR	December 1979	December 1979
Czechoslovakia	December 1978	December 1978

5. The term of the first inspection is 1981, the frequency of the inspection is 5 years.

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

And what is a round number in general? This is the one that ends in 0 (for the most part). In everyday life, the ability to round numbers makes shopping much easier. Standing at the checkout, you can roughly estimate the total cost of purchases, compare how much a kilogram of a product of the same name costs in packages of different weight. With numbers reduced to a convenient form, it is easier to make oral calculations without resorting to a calculator.

Why are numbers rounded?

A person is inclined 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 the southern fruit has, he may not be considered very well interesting companion... Phrases like "Here I bought a three-kilogram melon" sound much more laconic without delving into any 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 round them off as usual. As a rule, the result is then slightly distorted. So how do you round off numbers?

A few important rules when rounding numbers

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

1. If the number of the required digit is in the range of 5-9, rounding is carried out upward.
2. If the number of the required digit is in the range of 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. This is the answer to the question of how to round numbers. Now let's look at some special cases. Actually, we figured out how to round a number to tens using this example. Now all that remains is to use this knowledge in practice.

How to round a number to integers

It often happens that there is a need to round off, 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 its 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 it becomes legal to round up to 6. 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 basic principle. In fact, everything happens in much the same way. If the digit that is in the second position after the decimal point is within 5-9, then it is removed altogether, 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" leaves, 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 are not in the habit of assessing the real cost of a product, which is actively exploited by marketers. Everyone knows the slogans of stocks like "Buy for just 9.99". Yes, we consciously understand that this is essentially ten dollars. Nevertheless, our brain is designed in such a way that it only perceives the first number. So the simple operation of bringing a number into a convenient form should become a habit.

Very often, rounding off allows for a better estimate of intermediate successes, expressed in numerical form. For example, a person began to earn 550 dollars a month. An optimist will say that it 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 a myriad of examples where the ability to round turns out to be incredibly useful. It is important to be creative and, if possible, not be loaded with unnecessary information. Then success will be immediate.