Mathematics is an exact science, everyone knows this from childhood. And sometimes even thoughts do not allow that often it operates with approximate values. But even the value of the known constant - the number "pi", equal to 3.14 and used in the calculations, is approximate. Most constants from the famous Bradis table are also rounded.
The need to round numbers
Numbers are rounded in cases where absolute accuracy is not needed or impossible.
Not only mathematicians are faced with the need to round numbers to the required bit depth for convenience, and sometimes for the possibility of making calculations. A person is inclined to simplify his life, and when special accuracy of calculations is not required, he will undoubtedly round off any figure.
And in cases where in the intermediate calculation an infinite periodic fraction is obtained, further calculations are simply impossible without rounding off the obtained value. And the only way out is rounding to an acceptable bit depth.
That same famous “pi” is by default accepted in calculations with rounding to hundredths. If the condition of the assignment states "the number n round to tenths", then its value will be 3.1.
When solving problems from the school textbook, the accuracy of calculations is taken by default to the level of hundredths. Unless the condition of the problem says "round the numbers to the place of tenths."
Rounding numbers
Rounding a number is a mathematical operation to reduce the number of characters in a number and replace it with an approximate value of a given accuracy. It is performed by zeroing the significant digits to the right to the specified digit. Depending on the digit in the original number after the digit of the digit to which the number is to be excluded, the last significant digit of the rounded number can be equal to the digit of the original number, or increased by one.
If the first nullable digit after the digit of a given digit is less than or equal to 5, then the last stored digit does not change. If more than five, the last stored digit is incremented by one.
Rounding integers
An integer, or natural number, can be rounded to tens, hundreds, thousands, and so on. If a natural number needs to be rounded to tens, then the digit in the category of units is replaced by zero, and the digit in the category of tens is either left unchanged, or increased by one, if the original number in the category of units was the number 5 or more.
Rounding Fractional Numbers
Fractional numbers are rounded according to the same rules. If you want to round the original number to the category of tenths, then in the total number, there must be one digit after the decimal point. Determining which one is similar to determining the last digit when rounding a natural number.
Let's look at examples.
Example 1. How to round a number to tenths?
The original number is 108.039. The correct answer would be 108.0, since the digit of the hundredth digit is zero. The next one is 3, an increase is not required.
Example 2. How to round a number to tenths?
The original number is 108.89. The correct answer would be 108.9, since the number of the hundredth digit is more than five. According to rounding rules, an increase of the previous figure by one is required.
Example 3. How to round a number to tenths?
The original number is 108.0489. The correct answer in this case is 108.0, since according to the rules, rounding is not performed sequentially, starting with the last significant digit of the number, but the digit of the hundredth digit is considered.
But it’s important to remember that, even if you end up with a “0” after the decimal point, you must write it down, otherwise the decision will be erroneous. Without a decimal place, you will get a natural number, and in the conditions of the job, rounding to the tenth place was required.
Example 4. How to round a number to tenths?
The original number is 107.99. The correct answer is 108.0.
In this case, the number zero after the decimal point indicates that the number is rounded precisely to the place of tenths.