What is truncating in number system?

Answer 1

Truncating refers to the procedure of reducing the number digits of a decimal number. Trunkating to, say, 4 decimal digits results in the number 3.14159 being changed to 3.1415. Any digits past the four digits are simply ignored. Note that this is not the same as rounding, where the value of the first digit discarded is significant. Rounding normally reduces the error compared to trunkating. For information, the text below considers rounding as opposed to trunkating.

Rounding a number

The generally accepted rule is if the the last digit in the number string to the right of the decimal point is 5, 6, 7, 8, or 9, then round the number immediately to the left up to the next larger number; if the last digit in the number string is 0, 1, 2, 3, or 4, leave the number immediately to the left as it is.

Let's look at an example to see how this would work.

Assume you're doing some math problems and your teacher says "Give me your answers rounded to four (4) digits past the decimal point."

Let us use the same number we trunkated above: 3.14159. As you can see, your number has five (5) numbers past the decimal point.

Look at the very last digit, or in our example the "9."

3.14159

Using the rule above, the 9 and round the 5 (the number immediately to the left of 9) to 6, and your answer is:

3.1416

Suppose, however, next your calculation resulted in a product of 15.70795. Again, look to the last digit - in this case, "5."

15.70795

Again, referring to the generally accepted rule, the 5 is dropped and 9 (the number immediately to the left of 5) is rounded up to 10. But, since we need only four (4) digits past the decimal point, then your answer becomes:

15.708

Last example: suppose your calculation result in a product of 21.99113. Look to the last digit - "3."

21.99113

Using the generally accepted rule, drop the 3 and leave the 1 (the number immediately to the left of 3) as it is. Your answer is:

21.9911