How to Round Decimals
Understand the idea of decimal places., Find the decimal place you need to round to., Look at the number in the space to the right., If this number is greater than or equal to five, round up., If this number is less than five, round down., Use the...
Step-by-Step Guide
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Step 1: Understand the idea of decimal places.
In any number, the different digits represent different amounts.
For instance, in the number 1,872, the "1" represents thousands, the "8" represents hundreds, the "7" represents tens, and the "2" represents ones.
When there is a decimal point in a number, the numbers to the right of the point represent fractions of one.
The places to the right of the decimal point have names that mirror the names of the whole number decimal places.
The first number to the right of the decimal point represents tenths, the second represents hundredths, the third represents thousandths, and so on for ten-thousandths, etc.For example, in the number
2.37589, "2" is the number of ones, "3" is the number of tenths, "7" is the number of hundredths, "5" is the number of thousandths, "8" is the number of ten-thousandths, and "9" is the number of hundred-thousandths. -
Step 2: Find the decimal place you need to round to.
The first step to rounding a decimal is to determine which decimal place you're going to round it to.
If you're doing schoolwork, this information is usually given to you — often, the problem will say something like, "round the answer to the nearest tenth/hundredth/thousandth." For example, if you are asked to round to the nearest thousandth in the number
12.9889, you would start by finding the thousandths place.
Counting from the decimal point, the spaces to the right represent tenths, hundredths, thousandths, and ten-thousandths, so the second "8" (12.9889) is the one you want.
Sometimes, instructions will tell you exactly which decimal place to round to (e.g., "round to the third decimal place" means the same thing as "round to the nearest thousandth"). , Now, find the decimal place to the right of the place you're rounding to.
Based on the number in this place, you'll round either up or down.
In our example number (12.9889), you're rounding to the thousandths place (12.9889), so now look at the number to the right of this, which is the final "9" (12.9889). , To be clear: if the place you're rounding to is followed by a 5, 6, 7, 8, or 9, round it up.
In other words, make that decimal place one value greater and get rid of the digits after it.
In the example number (12.9889), since the final 9 is higher than 5, round your thousandths place up.
The rounded value becomes
12.989.
Note that you drop the digits after the rounded decimal place. , On the other hand, if the place you're rounding to is followed by a 4, 3, 2, 1, or 0, round it down.
This means to leave the rounded digit as it is and get rid of the digits after it.
You wouldn't round
12.9889 down because the final 9 isn't 4 or lower.
However, if you were working with the number
12.9884, you could round it down to
12.988.
Does this process seem familiar? If so, it's because this is basically how you round whole numbers — the decimal point doesn't change things. , One common rounding task is to round a number to the nearest whole number (sometimes, this will be explained as "rounding the number to the ones place").
In this case, use the same rounding technique as before.
In other words, start at the ones place, then look at the number to the right.
If this number is 5 or greater, round up.
If it is 4 or lower, round down.
The decimal point in the middle doesn't change anything.
For example, if you needed to round the example number from earlier (12.9889) to the nearest whole number, you'd start by looking at the ones place:
12.9889.
Since the "9" to the right is greater than 5, you would round up to
13.
Since you've gotten a whole number answer, you don't need the decimal point any more. , The directions for rounding above will work well in general.
However, when you've been given special directions for rounding decimal places, make sure to follow them before you use the normal rounding rules.
For example, if you receive the instructions "Round
4.59 down to the nearest tenth"
you'd round the 5 in the tenths place down even though the 9 to the right means you'd normally round it up.
This would give you
4.5.
Similarly, if you are told to "round
180.1 up to the nearest whole number," you'd round to 181 even though you'd normally round down. , See below for the solution.
First, find the hundredths place.
This is two spaces to the right of the decimal point, or
45.783.
Then, look at the number to the right:
45.783 Since 3 is less than 5, round down.
This gives an answer of
45.78. , Remember that "third decimal place" means to count three spaces to the right of the decimal point.
This is the same thing as saying "thousandths place." See below for the solution:
Find the third decimal place.
This is
6.2979.
Look at the number to the right.
This is
6.2979.
Since 9 is greater than 5, round up.
This gives an answer of
6.298. , The "0" here makes this one a little tricky, but remember that zeroes count as numbers less than four.
See below for the solution:
Find the tenths place.
This is
11.90.
Look at the number to the right.
This is
11.90.
Since 0 is less than 5, round down.
This gives an answer of
11.9. , Don't be intimidated by the negative sign — rounding negative numbers works exactly the same way as rounding positive numbers.
Find the ones place.
This is
-8.7 Look at the number to the right.
This is
-8.7.
Since 7 is greater than 5, round up.
This gives an answer of
-9.
Leave the negative sign as-is. -
Step 3: Look at the number in the space to the right.
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Step 4: If this number is greater than or equal to five
-
Step 5: round up.
-
Step 6: If this number is less than five
-
Step 7: round down.
-
Step 8: Use the same technique to round to a whole number.
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Step 9: Look out for special instructions.
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Step 10: Round 45.783 to the nearest hundredth.
-
Step 11: Round 6.2979 to the third decimal place.
-
Step 12: Round 11.90 to the nearest tenth.
-
Step 13: Round -8.7 to the nearest whole number.
Detailed Guide
In any number, the different digits represent different amounts.
For instance, in the number 1,872, the "1" represents thousands, the "8" represents hundreds, the "7" represents tens, and the "2" represents ones.
When there is a decimal point in a number, the numbers to the right of the point represent fractions of one.
The places to the right of the decimal point have names that mirror the names of the whole number decimal places.
The first number to the right of the decimal point represents tenths, the second represents hundredths, the third represents thousandths, and so on for ten-thousandths, etc.For example, in the number
2.37589, "2" is the number of ones, "3" is the number of tenths, "7" is the number of hundredths, "5" is the number of thousandths, "8" is the number of ten-thousandths, and "9" is the number of hundred-thousandths.
The first step to rounding a decimal is to determine which decimal place you're going to round it to.
If you're doing schoolwork, this information is usually given to you — often, the problem will say something like, "round the answer to the nearest tenth/hundredth/thousandth." For example, if you are asked to round to the nearest thousandth in the number
12.9889, you would start by finding the thousandths place.
Counting from the decimal point, the spaces to the right represent tenths, hundredths, thousandths, and ten-thousandths, so the second "8" (12.9889) is the one you want.
Sometimes, instructions will tell you exactly which decimal place to round to (e.g., "round to the third decimal place" means the same thing as "round to the nearest thousandth"). , Now, find the decimal place to the right of the place you're rounding to.
Based on the number in this place, you'll round either up or down.
In our example number (12.9889), you're rounding to the thousandths place (12.9889), so now look at the number to the right of this, which is the final "9" (12.9889). , To be clear: if the place you're rounding to is followed by a 5, 6, 7, 8, or 9, round it up.
In other words, make that decimal place one value greater and get rid of the digits after it.
In the example number (12.9889), since the final 9 is higher than 5, round your thousandths place up.
The rounded value becomes
12.989.
Note that you drop the digits after the rounded decimal place. , On the other hand, if the place you're rounding to is followed by a 4, 3, 2, 1, or 0, round it down.
This means to leave the rounded digit as it is and get rid of the digits after it.
You wouldn't round
12.9889 down because the final 9 isn't 4 or lower.
However, if you were working with the number
12.9884, you could round it down to
12.988.
Does this process seem familiar? If so, it's because this is basically how you round whole numbers — the decimal point doesn't change things. , One common rounding task is to round a number to the nearest whole number (sometimes, this will be explained as "rounding the number to the ones place").
In this case, use the same rounding technique as before.
In other words, start at the ones place, then look at the number to the right.
If this number is 5 or greater, round up.
If it is 4 or lower, round down.
The decimal point in the middle doesn't change anything.
For example, if you needed to round the example number from earlier (12.9889) to the nearest whole number, you'd start by looking at the ones place:
12.9889.
Since the "9" to the right is greater than 5, you would round up to
13.
Since you've gotten a whole number answer, you don't need the decimal point any more. , The directions for rounding above will work well in general.
However, when you've been given special directions for rounding decimal places, make sure to follow them before you use the normal rounding rules.
For example, if you receive the instructions "Round
4.59 down to the nearest tenth"
you'd round the 5 in the tenths place down even though the 9 to the right means you'd normally round it up.
This would give you
4.5.
Similarly, if you are told to "round
180.1 up to the nearest whole number," you'd round to 181 even though you'd normally round down. , See below for the solution.
First, find the hundredths place.
This is two spaces to the right of the decimal point, or
45.783.
Then, look at the number to the right:
45.783 Since 3 is less than 5, round down.
This gives an answer of
45.78. , Remember that "third decimal place" means to count three spaces to the right of the decimal point.
This is the same thing as saying "thousandths place." See below for the solution:
Find the third decimal place.
This is
6.2979.
Look at the number to the right.
This is
6.2979.
Since 9 is greater than 5, round up.
This gives an answer of
6.298. , The "0" here makes this one a little tricky, but remember that zeroes count as numbers less than four.
See below for the solution:
Find the tenths place.
This is
11.90.
Look at the number to the right.
This is
11.90.
Since 0 is less than 5, round down.
This gives an answer of
11.9. , Don't be intimidated by the negative sign — rounding negative numbers works exactly the same way as rounding positive numbers.
Find the ones place.
This is
-8.7 Look at the number to the right.
This is
-8.7.
Since 7 is greater than 5, round up.
This gives an answer of
-9.
Leave the negative sign as-is.
About the Author
Brittany Hayes
Writer and educator with a focus on practical organization knowledge.
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