Rounding Decimal Numbers Methods

Rounding Decimal Numbers

Rounding decimal numbers is a common practice used to simplify calculations by approximating values with a specific degree of precision. In this guide, we'll explore two important methods of rounding, which involve rounding to the nearest whole number and rounding to the nearest tenth.

Rounding to the Nearest Whole Number

When we round to the nearest whole number, our goal is to find the closest integer from a given decimal value without going over it. For example, if you have $7.8$, we can round it up to become $8$ because $8$ is the next highest integer closer to $7.8$. Here's how to do this systematically using the following steps:

1. Identify the digit right after the last retained digit. This will either be a $5$ or any other non-$9$ digit. If it's a $5$, go to step 2; otherwise, leave the retained digits unchanged.

   • Example: For $7.8$, the digit right after the tenths place ($0$) is (5), so proceed to step 2.

2. Increase the retained digits by one.

   • Example: For $7.8$, changing the tenths place to (1) gives us (7.9).

3. Check whether the new value lies within acceptable bounds based on the initial number. If it does, stop; otherwise, make the final change to retain only the desired number of decimals.

   • Example: Since (7.9 > 7.8), it exceeds the original fractional part, requiring adjustment. We keep the ones place ((9 \rightarrow 8)), maintaining the rounded result of (8).

Examples

Note: To round towards zero instead of always away from zero, you would decrease the retained digits when they equal (5).

Rounding to the Nearest Tenth

While rounding to the nearest whole number provides approximate integers, sometimes more precise estimates are needed. When dealing with fractions of a unit, such as in measurement or currency problems, rounding to the nearest tenth allows for better accuracy while still being manageable.

Similar to rounding to the nearest whole number, we follow these simple rules when approaching the task:

1. Identify the digit right after the last retained digit. This will either be a (5) or any other non-(9) digit. If it's a (5), go to step 2; otherwise, leave the retained digits unchanged.

   • Example: For (7.83), the hundreds place ((3)) is the retained digit right after the tenths place ((8)). It equals (5), so move to step 2.

2. Increase the retained digits by one.

   • Example: Changing the tens of thousandths place ((3)) into (4) results in (7.84).

3. Check whether the new value lies within acceptable bounds based on the initial number. If it does, stop; otherwise, adjust the additional digits accordingly.

   • Example: Since (7.84 > 7.83), it exceeds the original fractional part, requiring adjustment. We reduce the hundredths place (from (4 \rightarrow 4 - 1 = 3)), retaining (7.83) as the final answer.

Examples

With practice, rounding to both the nearest whole number and nearest tenth becomes second nature, making your mathematical calculations simpler and more accurate.