Nobody likes to do calculations with long and complex rows of decimals, so a technique called "rounding" (or sometimes "estimation") is used to simplify numbers and make calculations easier. Rounding a decimal number is very similar to rounding an integer; you just have to find the place value you want to round to and look at the figure to its right. If this is equal to or greater than 5, rounds up.
If it's less than 5, rounds down.
Steps
Part 1 of 2: Instructions for Rounding
Step 1. Learn to recognize decimal positional values
In all numbers, the different digits represent different quantities. For example, in the number 1872, the "1" represents thousands, the "8" represents hundreds, the "7" represents tens, and the "2" represents units. When a number contains a comma (or decimal point), the numbers to the right of the comma represent fractions of the unit.
- The positional values to the right of the comma have names that mirror those of the digits of the integers. The first digit to the right of the comma represents i tenths, the second represents i cents, the third represents i thousandths and so on for tenths of a thousandth, etc.
- For example, in the number 2, 37589, "2" represents the units, "3" the tenths, "7" the hundredths, "5" the thousandths, "8" the tenths of a thousandth and "9" the hundredths of a thousandth.
Step 2. Find the decimal place value to round
The first step in rounding a decimal number is to determine which decimal place value you will round. If you are doing your homework, you are usually told this; often the problem says something like: “Round the result to the nearest tenth / hundredth / thousandth”.
-
For example, if you are asked to round the number 12 to the nearest thousandth, 9889 will start by determining where the thousandths are. Counting from the comma, the figures on the right represent tenths, hundredths, thousandths and tenths of a thousandth, hence the second "8" (12, 98
Step 8.9) is the number you are looking for.
- Sometimes, the instructions will tell you exactly which decimal place to round (for example, "round to the third decimal place" has the same meaning as "round to the nearest thousandths").
Step 3. Look at the number to the right of the one to round
Now, determine which digit is to the right of the decimal you need to round. Based on the value of that figure, you will round up or down.
-
In our example (12, 9889), you need to round thousandths (12, 98
Step 8.9), then you will look at the digit to their right, which is the last "9" (12, 98
Step 9.).
Step 4. If this number is greater than or equal to 5, round up
To clarify: if the figure you need to round is followed by a 5, 6, 7, 8 or 9, round it up. In other words, it increases the digit by 1 and eliminates the following ones.
In our example (12, 9889), since 9 is greater than 5, it rounds the thousandths for excess. The rounded number will be 12, 989. Note that you no longer wrote the digits that followed the rounded digit.
Step 5. If this number is less than 5, round down
If the digit to be rounded is followed by 4, 3, 2, 1 or 0, round it down. This means leaving the rounding figure as it is and eliminating the subsequent figures.
-
You will not round 12.9889 down, because 9 is not less than or equal to 4. If the number were 12, 988
Step 4., you could have rounded it to 12, 988.
- Does this process seem familiar to you? If so, it's because it's basically the same process as you round whole numbers: the comma doesn't change it.
Step 6. Use the same method to round to an integer
A commonly required task is to round a decimal number to the nearest integer (sometimes the problem will tell you to "round the number to units"). In this case, use the same method that was applied earlier.
- In other words, start with the units and look at the figure to their right. If this number is greater than or equal to 5, it rounds up; if it is equal to or less than 4, round down. The presence of the comma between the two numbers does not change anything.
-
For example, if you had to round the number in the previous example (12, 9889) to the nearest whole number, you would have started by looking at the units: 1 2, 9889. Since the "9" on the right is greater than 5, you would have rounded up to
Step 13.. Since you got an integer as a result, you no longer need the comma.
Step 7. Look for specific indications
The rules for rounding explained above work well in general; however, if you are given specific instructions for rounding decimals, be sure to follow them before using the general rules.
- For example, if you are told to "round 4, 59 by default to the nearest tenth ", you will round the 5 which represents the tenths down, although normally the 9 to its right would make you round it up. You would get as a result 4, 5.
- Likewise, if you were told to "round 180, 1 for excess to the nearest whole number ", you would round it to 181 even though you would normally have rounded it down.
Part 2 of 2: Examples
Step 1. Round 45, 783 to the nearest hundredths
Read the solution below:
-
First, identify the cents: they are represented by the second digit to the right of the decimal point, which is 45, 7
Step 8.3.
-
Then, look at the figure on the right: 45, 78
Step 3.
- Since 3 is less than 5, it rounds down. Get as a result 45, 78.
Step 2. Rounds 6, 2979 to the third decimal place
Remember that "third decimal place" means to count three digits to the right of the decimal point. It is the same as identifying "thousandths". Read the solution below:
-
Find the third decimal place. It is 6, 29
Step 7.9.
-
Look at the figure on the right. It is 6, 297
Step 9..
- Since 9 is greater than 5, it rounds up. Get as a result 6, 298.
Step 3. Round 11.90 to the nearest tenths
Here the "0" makes it a little more complex, but remember that zeros count as numbers less than 5. Read the solution below:
-
Find the tenths. The figure is 11,
Step 9.0.
- Look at the figure on the right. It is 11, 9 0.
- Since 0 is less than 5, it rounds down. Get as a result 11, 9.
Step 4. Round -8, 7 to the nearest whole number
Don't be intimidated by the minus sign - negative numbers round up just like positive numbers.
-
Search for units. The figure is -
Step 8., 7
-
Look at the figure on the right. It is -8,
Step 7..
-
Since 7 is greater than 5, it rounds up. Get as a result -
Step 9.. Leave the minus sign as it is.
Advice
- If you have difficulty with decimal placement values, look for a guide on the internet.
- You can also find tools online to automatically round numbers, which can be useful if you are dealing with numbers with many digits.
