What rule allows us to round decimal numbers? And what is the difference between rounding and truncating?
I. Rounding to the nearest unit
Example: In figure 1, we have placed the numbers 8, 8.36, 8.5, 8.74, and 9 on an axis.As 8.36 is closer to 8 than to 9, when we round 8.36 to the nearest unit we get the number 8.
For a similar reason, when we round 8.74 to the nearest unit, we get the number 9.
For the number 8.5, we must make a choice, because it is positioned at the same distance from 8 and from 9. We will decide to choose 9 when we round 8.5 to the nearest unit.
Definition: a is a decimal number:
When the decimal part of a is 0.5, rounding to the nearest unit gives us the integer just greater than a;
in other cases, rounding a to the nearest unit gives us the whole number that is closest to a.
II. Truncating to the unit
Example: Figure 2 shows a way of truncating the number 31.42 to the unit. This truncation gives us 31. We just need to “cut off the decimal part” of the number.
Definition: Truncating a decimal number d to the unit gives the largest integer less than or equal to d.
Therefore there are two possibilities:
The truncation is equal to rounding to the nearest unit (this is the case for 8.36);
the truncation is equal to 1 less than rounding to the nearest unit (this is the case for 8.74).
Read more:
Applying the Distributive Law
Calculating a Numerical Expression (1)
Calculating a Numerical Expression (2)
Determining the Common Factors of Two Integers
Recognizing a Proportional Relationship
Writing a Numerical Expression That Corresponds to a Sequence of Operations