The concept and term “*rounding off*” is the process of simplifying a number by bringing the number closer to the next number and keeping its value.

In most of the everyday situations, we do not need to use highly sensitive measuring devices (instruments). the accuracy of our measurement depends on the purpose for which we use the information.

Example: Suppose someone uses a compass as a guide in going from one end of the school to the other. It would not be a serious error if he/ she is 1o of course. However, 1o of course on a journey to the moon will mean an error of 644000 km.

Besides the error arising from the use of different instruments/ devices, the person taking the measurement is another source of error. For example, in school/ college athletics meets, there are usually two or more time-keepers for the first placing of a (say) 100-meter race, and time-keepers may have slightly different times on their devices (such as sports watch). Therefore, all physical measurements such as mass, length, time, volume, and area can never be accurate. The accuracy depends on the degree of the measuring device (instrument) and the person recording (taking) the measurement. Both of them can never be accurate.

### Rules for Rounding off Numbers

**Rule 1:** Determine what your rounding digit is and look at the digit to the right of it. If the number is 1, 2, 3, or 4, simply drop all digits to the right of the rounding digit. For example,

5.432 may be rounded off to 5.42 nearest to the hundredth place.

5.432 may be rounded off to 5.4 nearest to the tenth place.

5.432 may be rounded off to 5 nearest to the unit’s place.

**Rule 2:** Determine what your rounding digit is and look at the digit to the right of it. If the number is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of the rounding digits. For example,

3.786 may be rounded off to 3.79 nearest to the hundredth place.

3.786 may be rounded off to 3.8 nearest to the tenth place.

3.876 may be rounded off to 3.9 nearest to the unit place.