No mathematician likes to calculate long and confusing decimal numbers, so they often use a technique called "rounding" (or sometimes "estimation") to make calculating the number easier. Rounding decimal numbers is very similar to rounding whole numbers - just find the place value that needs to be rounded, and look at the number to the right. If five or greater, round up.
If smaller than five, round down.
Step
Part 1 of 2: Decimal Rounding Guide
Step 1. Understand the material about the place value of decimal numbers
In any number, the numbers in different places represent different values. For example, in 1872, the number “1” represents thousands, the number “8” represents hundreds, the number “7” represents tens, and the number “2” represents units. If there is a decimal point (comma) in the number, the number to the right of the decimal sign represents a fraction of one.
- The place value to the right of the decimal sign has a name that reflects the name of the integer place value to the left of the decimal sign. The first number to the right of the decimal sign represents tithe, the second number represents hundredths, the third number represents thousandths, and so for tenths of thousands, and so on.
- For example, in the number 2, 37589, the number “2” represents units, the number “3” represents tenths, the number “7” represents hundredths, the number “5” represents thousandths, the number “8” represents tenths of thousands, and the number “9” represents hundredths of thousands..
Step 2. Find the decimal place value that needs to be rounded
The first step in rounding a decimal number is to determine which decimal place value to round. When doing homework, this information is usually readily available, with sample questions such as "round the answer to the nearest tenth/hundredth/thousandth."
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For example, if you are asked to round the number 12.9889 to the nearest thousandth, start by finding the thousandth place value. Counting from the decimal point, the places to the right represent tenths, hundredths, thousandths, and tenths of a thousand, so the second “8” (12, 98)
Step 8.9) is the desired number.
- Sometimes, the question will say exactly how many decimal places are required. (example: “round to 3 decimal places” has the same meaning as “round to the nearest thousandth”).
Step 3. Look at the number to the right of the requested decimal place
Now, look at the decimal place to the right of the requested decimal place. Based on the number in this decimal place, the decimal number will be rounded up or down.
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In our example number (12, 9889), you are rounding to the thousandth place (12, 98
Step 8.9). So now, look at the number to the right of the thousandth place, which is the last "9" (12, 98.)
Step 9.).
Step 4. If the number is greater than or equal to five, round up
To be clear: if the decimal place to be rounded is followed by the number 5, 6, 7, 8, or 9, round up. In other words, make the required decimal place one value greater, and omit the numbers to the right of it.
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In the example number (12, 9889), since the last 9 is greater than 5, round to the thousandth place on.
The resulting number is rounded to 12, 989. Note that numbers to the right of the rounded decimal place must be omitted.
Step 5. If the number to the right of the requested decimal place is less than five, round down
On the other hand, if the place to be rounded is followed by the number 4, 3, 2, 1, or 0, round down. That means, the number that is rounded does not change, and the numbers to the right of it are omitted.
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The number 12, 9889 will not be rounded down because the last 9 is not a 4 or less. However, if you round the number 12, 988
Step 4., round down to 12, 988.
- Does this process sound familiar? If so, it's because this process is basically how you round integers, and the decimal sign doesn't change the rounding process.
Step 6. Use the same technique to round a decimal number to an integer
One common rounding problem is to round a decimal number to the nearest whole number (sometimes, the problem will sound like “round to the ones place”). In this problem, use the same rounding technique as before.
- In other words, start at the units place, then look at the number to the right of it. If the number is 5 or greater, round up. If it's 4 or less, round down. The decimal point in the middle does not change the rounding process.
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For example, if you need to round the sample number from the previous problem (12, 9889) to the nearest whole number, start by finding the ones place: 1
Step 2., 9889. Since the number “9” to the right of the units place is greater than 5, round the decimal number up to
Step 13.. Since the answer is already an integer, the decimal sign is no longer needed.
Step 7. Observe special instructions
The rounding guidelines described above are generally used. However, when you get a decimal number rounding problem with special instructions, make sure you follow those special instructions before the normal rounding rules.
- For example, if the question reads "round 4.59 to lower to the nearest tenth", round 5 in the lower tenth place, although the 9 to the right usually causes rounding up. So the answer to this particular problem is 4, 5.
- Likewise, if the question reads "round 180, 1 to on to the nearest integer", round to 181 although usually the number is rounded down.
Part 2 of 2: Sample Questions
Step 1. Round 45, 783 to the nearest hundredth
Here is the answer:
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First, find the hundredths place, which is two places to the right of the decimal point, or 45, 7
Step 8.3.
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Then, look at the numbers on the right: 45, 78
Step 3..
- Since the number 3 is less than 5, round the decimal number down. So, the answer is 45, 78.
Step 2. Round 6, 2979 to 3 decimal places
Keep in mind that “3 decimal places” means three places to the right of the decimal sign, which is the same as “thousandths place”. Here is the answer:
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Find the third decimal place, which is 6.29
Step 7.9.
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Look at the number to the right, which is 6,297
Step 9..
- Since 9 is greater than 5, round up the decimal number. So, the answer is 6, 298.
Step 3. Round 11, 90 to the nearest tenth
The number "0" here is a little confusing, but remember that zero counts as a number less than four. Here is the answer:
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Find the position of the tenths, which is 11,
Step 9.0.
- Look at the number to the right, which is 11, 9 0.
- Since 0 is less than 5, round down the decimal number. So, the answer is 11, 9.
Step 4. Round -8, 7 to the nearest integer
Don't worry too much about negative signs, because rounding negative numbers is the same as rounding positive numbers.
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Find the unit place, i.e. -
Step 8., 7
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Look at the number to the right, which is -8,
Step 7..
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Since 7 is greater than 5, round up the decimal number. So, the answer is -
Step 9.. Do not change the negative sign.
Tips
- If you're having trouble remembering some of the higher decimal place values, take a look at this handy guide.
- Another handy tool is this automatic rounding calculator, which can be helpful when calculating large numbers.
