# Rounding of numbers

Rounding of numbers used to work with numbers within the number of characters that correspond to the actual parameters of the calculation accuracy. In the past, rounding of intermediate values and the result had applied value (in the calculations on paper or using primitive devices such as the abacus accounting extra decimals can seriously increase the amount of work). Now it remains part of the scientific and engineering culture. The use of rounding in the accounting department, for example, intermediate, may be required for the protection of computer errors related to the final digit of computing devices.

In different areas may apply different methods of rounding. In all these methods, the "extra" signs are zeroed, the sign in front of them is adjusted by any rule.

Rounding is that one or more digits at the end of number is replaced with zeros. Since zeroes after the decimal point, do not matter, they are discarded. For example: 3734 rounded in 3730 or 3700, 5,314 - to 5,31 or 5,3, 0,00731 - 0,0073 or 0,007.

If the first digit is 6 or more, the previous number is incremented by one. For example: 4867 rounded in 4870 or 4900, 5989 or 5990 shall be rounded to 6000, 3,666 rounded to 3,67 or 3,7.

So do if discarded digit 5. For example: in 4552 rounded to 4600, 38,1506 rounded to 38,2.

So do if discarded number 5 followed by meaningless numbers. For example: 4552 rounded to 4600, 38,1506 rounded to 38,2.

But if discarded only figure 5, the increase by one of the preceding digit agreed, only when it is odd; the even number remain unchanged. For example: 735 rounded to 740, 8645 rounded to 8640, 37,65 – 37,6, 0,0275 – 0,028, 70,5 – 70 (zero is treated as an even number).

When you need a rough estimate of the number of accurate digits in the calculation result, it is possible to carry out the rounding of numbers with simple rules. All initial values are rounded to the real measurement accuracy and recorded with the appropriate number of significant digits, so that in decimal notation all numbers were reliable (it is allowed to the last digit was doubtful). If necessary, the values are written with meaningful right with zeros to the record indicated the actual number of reliable signs (e.g., if in 1 m length actually measured with an accuracy of centimeters, is written "1.00 m" to make it clear that the records are reliable two signs after the decimal point). Or accuracy is clearly indicated (for example, 2500± 5 m - is only ten are reliable to its should be rounded).