Approximate numbers

Who does not know what is the approximate number that is likely to be interesting at least briefly acquainted with them, the more that knowledge of simple techniques to work with approximate numbers is practically useful.

Who does not know what is the approximate number that is likely to be interesting at least briefly acquainted with them...

The exact solution of certain mathematical problems can not be obtained by classical methods, or the decision may be obtained in a very complex form, unacceptable for practical use. In addition, the exact solution of the problem requires, in this case, a very large number of mathematical operations.

Let us explain, first of all, what is the approximate number and where such numbers are obtained.

Any measurement can not be done exactly. First of all, the best measure is already used by measuring typically embody error. For example, in the manufacture of meter error range allowed by law to 1 mm. This is the approximate number.

The arithmetic of approximate numbers is not at all similar to the arithmetic of numbers accurate.

For example, we have an approximate number of 68 and 42. In other words, you can record 68,? and 42,?. Multiply the approximate numbers in a column and get the result: 68,? x 42,? = 285?,??. We can see that the fourth digit of the result is unknown to us: it should get from adding the three digits (? + 6 +?), two of which are unknown. We recorded 5, but by adding (? + 6 + ?). Could get a number greater than 10 and even 20; hence, instead of 5 may be 6 and 7. It is reliable, only the first two digits 28. Therefore, we can say that the result of the multiplication is the approximate number of about 28 hundred.

So, when is calculation with approximate numbers, it is necessary to take into account not all of the digits of result, but only some.

Let X is the exact value of a certain value, and the x is the best known of its approximate value. In this case, the error (or error) approximation of x is determined by the difference in X-x. Usually, the sign of this error is not critical, so consider it an absolute value. Digit number is called true, if its absolute error does not exceed the discharge unit, in which is the digit. Example. X = 6,328 X = 0,0007 X <0,001 so number 8 is true digit. First discarded (incorrect) digit often called questionable. It is said that the approximate number of recorded correctly, if in it all the numbers are correct. If the number is written correctly, the only of its record as a decimal fraction, you can judge the accuracy of this number.