Rounding Decimals: Guide and Examples

What Is Rounding Decimals?

Rounding decimals means shortening a number to a specific place value, such as the nearest tenth or hundredth. The rules are exactly the same as rounding whole numbers.

When a decimal is rounded, it becomes an approximation. We use the approximately equal symbol ($\approx$) to show that the exact value has been adjusted. For example, $4.83\approx 4.8$.

If the digit used to decide the rounding is small, the target digit remains unchanged, which is called rounding down. If the decision digit is large, the target digit increases by one, which is called rounding up.

When to Use It

Rounding decimals is an essential tool for estimation in math, allowing you to work with simpler numbers when exact values are unnecessary.

In everyday life, money is usually rounded to two decimal places, representing dollars and cents. Measurements such as distance, weight, or temperature are often rounded to one or two decimal places so they are easier to read and communicate. Rounding is also frequently used to shorten repeating decimals produced by a calculator.

Step-by-Step Method

Follow these numbered steps to round any decimal number:

1. Identify the target place value, such as the nearest whole number, tenth, or hundredth.
2. Look at the decision digit immediately to the right of the target place.
3. If the decision digit is $0$, $1$, $2$, $3$, or $4$, keep the target digit the same to round down.
4. If the decision digit is $5$, $6$, $7$, $8$, or $9$, add $1$ to the target digit to round up.
5. Remove all digits to the right of the target place.

decision digit is always exactly one place to the right of the target digit.

Visual Worked Examples

Example 1: Rounding to the nearest whole number

Question: Round $14.5$ to the nearest whole number.

Method:

1. The target place is the nearest whole number, which is the ones place containing $4$.
2. The decision digit to the right is $5$.
3. Because the decision digit is $5$, round up by adding $1$ to the $4$.
4. The $4$ becomes a $5$.
5. Remove the decimal point and all digits to the right.

Answer: $15$.

Check: On a number line, $14.5$ is exactly halfway between $14$ and $15$. By mathematical convention, a midpoint always rounds up.

Example 2: Rounding to the nearest tenth with a 9

Question: Round $6.97$ to the nearest tenth.

Method:

1. The target place is the tenths place, which contains $9$.
2. The decision digit to the right is $7$.
3. Because the decision digit is $7$, round up by adding $1$ to the $9$.
4. Adding $1$ to $9$ tenths makes $10$ tenths, which regroups as $1$ whole. The $6$ becomes a $7$, and the $9$ becomes a $0$.
5. Remove all digits to the right of the tenths place.

Answer: $7.0$.

Check: The number $6.97$ is closer to $7.0$ than to $6.9$. The zero must be written to show the number was rounded to the tenths precision.

Example 3: Rounding to the nearest hundredth and thousandth

Question: Round $3.14159$ to the nearest hundredth, and then round the original number to the nearest thousandth.

Method:

1. To round to the nearest hundredth, the target digit is $4$ and the decision digit is $1$.
2. Because $1$ is less than $5$, keep the $4$ and remove the following digits to get $3.14$.
3. To round to the nearest thousandth, the target digit is the $1$ in the thousandths place and the decision digit is $5$.
4. Because the decision digit is $5$, round up by adding $1$ to the target digit to get $2$.
5. Remove the digits after the thousandths place to get $3.142$.

Answer: The nearest hundredth is $3.14$. The nearest thousandth is $3.142$.

Check: The number $3.14159$ is closer to $3.142$ than to $3.141$.

How to Check the Answer

The most reliable way to check a rounded decimal is to find the exact midpoint between the two possible rounded values. A number line check helps you determine if the original number is greater than less than equal to the halfway mark.

If you are rounding $8.23$ to the nearest tenth, the two possible answers are $8.2$ and $8.3$. The exact midpoint is $8.25$. Compare the original number to the midpoint. Because $8.23$ is less than $8.25$, it sits on the lower half of the number line and rounds down to $8.2$.

Common Mistakes

A frequent error is chain-rounding, where a student looks too far to the right and rounds multiple times. To round $7.449$ to the nearest tenth, you must look only at the hundredths digit, which is $4$. The number rounds down to $7.4$. You should never round the $4$ up to $5$ just because of the $9$.

Another mistake occurs when students incorrectly drop trailing zeros. If a calculation requires rounding $12.98$ to the nearest tenth, rounding up changes the $9$ to a $0$ and carries $1$ to the whole number, giving $13.0$. Writing the answer merely as $13$ changes the precision of the result. Retaining the correct number of decimal places becomes critical when evaluating significant figures in later mathematics.

Finally, take care when comparing and ordering numbers that have been rounded. Rounding changes the exact value slightly, meaning two different numbers might round to the same decimal, or a previously smaller number could appear equal to a larger one.