Many situations require you to round a decimal number to the nearest tenth to make the number easier to work with. Once you understand how to find the tenths and hundredths place, the process is the same as for rounding whole numbers.
Step
Part 1 of 2: Round to the Nearest Tithe
Step 1. Review rounding on the number line (optional)
Ignore the decimals for a while and try rounding to the tenth place. Draw a number line from 10 to 20. Numbers on the left half of the number line (such as 13 or 11) are closer to 10 so they are rounded off to 10. Numbers on the right half of the number line (such as 16 or 17)) is closer to 20 so it's rounded to 20. Rounding decimals seems confusing, but it's actually the same process. You can re-label the number line with “0, 10, 0, 11, 0, 12, …, 0, 19, 0, 2” and you will have a number line for rounding to the nearest tenth.
Step 2. Write down the number with a decimal point
The number of digits after the decimal is not a problem.
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Example 1:
Round 7.86 to the nearest tenth.
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Example 2:
Round 247, 137 to the nearest tenth.
Step 3. Find the place of the tithe
The tenth place is directly to the right of the decimal point. After rounding to the nearest tenth, this number will be the last digit of your number. For now, just underline this digit.
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Example 1:
At the number 7, 86,
Step 8. is in the tithes.
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Example 2:
At the numbers 247, 137,
Step 1. be in the tithes.
Step 4. Look at the hundredth place
The hundredth place is the second digit to the right of the decimal point. This digit tells you whether you should round up or down.
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Example 1:
At 7, 86,
Step 6. was in the hundredth place.
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Example 2:
At 241, 137,
Step 3. was in the hundredth place.
- The digits to the right of the hundredths place don't matter if you're rounding to the nearest tenth. The digits represent an "additional value" indicating a small difference.
Step 5. Round up the tenth place if the hundredth place is 5 or more
Are the digits in the hundredths place 5, 6, 7, 8, or 9? If so, “round up” by adding 1 to the tenth place digit. Erase all the digits after the tenth place and you've got your answer.
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Example 1:
The hundredths place of 7, 86 is 6. Round up by adding 1 to the tenths place (8) to get 7, 9 and delete the digits to the right.
Step 6. Round the tenth place down if the hundredth place is 4 or less
Are the digits in the hundredths place 4, 3, 2, 1, or 0? If so, “round down” leaving the tenth place. Erase the digits in the hundredths place and to the right of them.
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Example 2:
The hundredths place of 247, 137 is 3. Round down by removing all digits to the right of the tenth place to get 247, 1.
Part 2 of 2: Special Case
Step 1. Round the number down to zero in the tenth place
If there is a zero in the tenth place and you are rounding down, just leave the zero in your answer. For example, 4, 03 rounded to the nearest tenth to 4, 0. This rounding indicates the accuracy of your number. Just writing "4" isn't wrong, but it will hide the fact that you're working with decimal numbers.
Step 2. Round up negative numbers
Basically, rounding negative numbers is the same as rounding positive numbers. Follow the same process and remember to always put a negative sign in your answers. For example, -12, 56 is rounded up to -12, 6 and -400, 333 is rounded up to -400, 3.
Be careful using the phrases “round down” and “round up”. If you look for negative numbers on the number line, you'll notice that the rounding of -12, 56 to -12, 6 moves to the left. As such, this process is “rounding down” even if you add one to the tenth digit
Step 3. Round up very long numbers
Don't get confused by very long numbers. The rules remain the same. Find the tenth place and decide whether you should round up or down. After rounding off, all numbers to the left of the tenth place remain the same, while all numbers to the right of the tenth place disappear. Consider the following three examples:
- 7192403242401, 29 is rounded to 7192403242401, 3
- 5, 0620138424107 rounded to 5, 1
- 9000, 30001 rounded up to 9000, 3
Step 4. Leave only the numbers that don't have a hundredth place
Does the number end in the tenth place and have no other number to the right? If so, this number has already been rounded to the nearest tenth so you don't have to do anything else. The textbook may be trying to trick you.
