Multiplication of a monomial by a polynomial is a new material. Lesson "multiplying a monomial by a polynomial"

In mathematics, rounding is an operation that allows you to reduce the number of characters in a number by replacing them, taking into account certain rules. If you are interested in the question of up to hundredths, then first you should deal with all the existing rounding rules. There are several options for how you can round numbers:

Statistical - used to clarify the number of residents of the city. Speaking about the number of citizens, they only give an approximate value, and not an exact figure.
Half - half is rounded to the nearest even number.
Rounding up fewer(rounding towards zero) - this is the easiest rounding, in which all "extra" digits are discarded.
Rounding up more- if the signs that want to be rounded are not equal to zero, then the number is rounded up. This method is used by providers or mobile operators.
Non-zero rounding - numbers are rounded according to all the rules, but when the result should be 0, then rounding is performed "from zero".
Alternating rounding - when N + 1 equals 5, the number is alternately rounded up and down.

For example, you need to round the number 21.837 to the nearest hundredth. After rounding, your correct answer should be 21.84. Let's explain why. The number 8 is in the category of tenths, therefore, 3 is in the category of hundredths, and 7 is in thousandths. 7 is greater than 5, so we increase 3 by 1, that is, up to 4. It's really easy if you know a few rules:

1. The last stored digit is increased by one if the first one discarded before it is greater than 5. If this digit is equal to 5 and there are some other digits after it, then the previous one also increases by 1.

For example, we need to round to tenths: 54.69=54.7, or 7.357=7.4.

If you are asked a question about how to round a number to the hundredth, proceed in the same way as the above option.

2. The last retained digit remains unchanged if the first discarded digit that precedes it is less than 5.

Example: 96.71=96.7.

3. The last digit to be retained remains unchanged, provided that it is even, and if the first digit to be discarded is the number 5, and there are no more digits after it. If the remaining digit is odd, then it is increased by 1.

Examples: 84.45=84.4 or 63.75=63.8.

Note. Many schools give students a simplified version of the rounding rules, so it's worth keeping that in mind. In them, all the numbers remain unchanged if they are followed by numbers from 0 to 4 and increase by 1, provided that after them there is a number from 5 to 9. Competently solve problems with rounding according to strict rules, but if a simplified version is introduced at school, then in order to avoid misunderstandings, it is worth sticking to it. We hope you understand how to round a number to hundredths.

Rounding in life is necessary for the convenience of working with numbers and indicating the accuracy of measurements. Currently, there is such a definition as anti-rounding. For example, when counting the votes of a study, round numbers are considered bad manners. Stores also use anti-rounding to give shoppers the impression of a better price (say 199 instead of 200, for example). We hope that now you can answer the question of how to round a number to hundredths or tenths yourself.

Understand the meaning of numbers in decimals. In any number various numbers are different categories. For example, in the number 1872, one represents thousands, eight represents hundreds, seven represents tens, and two represents ones. If there is a decimal point in the number, then the numbers to the right of it reflect fractions of a whole number.

Determine the decimal place to which you want to round it. The first step in rounding decimals is determining the place to which you want to round a number. If you do homework, then this is usually determined by the task condition. Often, the condition may indicate the need to round the answer to tenths, hundredths, or thousandths of a decimal point.

For example, if the task is to round the number 12.9889 to thousandths, you should start by identifying the location of these thousandths. Count the decimal places as tenths, hundredths, thousandths, followed by ten thousandths. The second eight will be just what you need (12.98 8 9).
Sometimes a condition may specify where to round (for example, "round to three decimal places" means the same as "round to thousandths").

Look at the number to the right of where you want to round off. Now you should find out the number that is to the right of the place to which you are rounding. Depending on this figure, you will round up or down (up or down).

In the example of the number (12.9889) taken earlier, it is necessary to round to thousandths (12.98 8 9), so now you should look at the number to the right of the thousandth, namely the last nine (12.988 9 ).

If this figure is greater than or equal to five, then rounding up is performed. For greater clarity, if the number 5, 6, 7, 8 or 9 is to the right of the rounding point, then rounding up is performed. In other words, it is necessary to increase the digit at the rounded place by one, and discard the remaining digits to the right of it.

In the example taken (12.9889), the last nine is greater than five, so we will round the thousandths to the big side. The rounded number will appear as 12,989 . Note that after the rounding point, the figures are discarded.

If this figure is less than five, then rounding down is performed. That is, if the number 4, 3, 2, 1 or 0 is to the right of the rounding point, then rounding down is performed. Which means the need to leave the figure in place of the rounding in the form in which it is, and discard the numbers to the right of it.

You cannot round down 12.9889 because the last nine is not a four or less. However, if the number in question were 12.988 4 , then it could be rounded up to 12,988 .
Does the procedure sound familiar? This is due to the fact that integers are rounded in the same way, and the presence of a comma does not change anything.

Use the same method to round decimals to integers. Often the task establishes the need to round the answer to integers. In this case, you must use the above method.

In other words, find the location of the integer units of the number, look at the number on the right. If it is greater than or equal to five, then round the whole number up. If it is less than or equal to four, then round the whole number down. The presence of a comma between whole part number and its decimal does not change anything.
For example, if you want to round the above number (12.9889) to integers, you would start by locating the integer units of the number: 1 2 .9889. Since the nine to the right of this place is greater than five, we round up to 13 whole. Since the answer is represented by an integer, there is no need to write a comma anymore.

Pay attention to rounding instructions. The above rounding instructions are generally accepted. However, there are situations where special rounding requirements are given, be sure to read them before resorting to the generally accepted rounding rules right away.

For example, if the requirements say to round down to tenths, then in the number 4.59 you will leave a five, despite the fact that a nine to the right of it should usually result in rounding up. This will give you the result 4,5 .
Similarly, if you are told to round the number 180.1 to whole to the big side, then you will succeed 181 .

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 up decimal up 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 to tenths given number, 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: