8
Step-by-step explanation:
Rounding is a process for reducing the number of non-zero digits in a number. It is used to create values that are "close enough" for many purposes. It is often used to simplify mental arithmetic, make estimation easier, or make the precision of a number better agree with its accuracy.
The nearest one refers to a specific digit location in the number. The digit locations in a decimal number have names. Some of them are shown on the chart below. After the number is rounded to the nearest one, all of the digits to the right of the ones place will be deleted. (When rounding to a number place to the left of the ones place, digits to its right are set to zero.)
Different methods are used for rounding in different circumstances. The one most commonly used (and generally expected to be used in your math class) is the one described here.
__
Step 1.
Find the digit immediately to the right of the one to which you are rounding. Here, you're rounding to the ones place, so the digit to its right is the digit in the tenths place. That digit is 2.
Step 2.
If the digit you found in Step 1 is 4 or less, proceed to step 4. Here, you proceed to Step 4, because the found digit is 2.
Step 3.
If the digit you found in Step 1 is 5 or more, add 1 to the number in the place to which you are rounding. For example, if you're rounding to the ones place, add 1; if you're rounding to the hundreds place, add 100.
Step 4.
Drop the digit to the right of the one you're rounding to, and all digits to its right. If any of these digits are to the left of the decimal point, set them to zero instead, so the place values of the remaining digits are preserved.
Here, you drop the tenths digit, leaving only the ones digit, so the result is 8.
Step 5.
If the number has a decimal point and you're rounding to a digit left of the ones place, the decimal point will be removed. If you're rounding to the ones place and the ones digit is non-zero, the decimal point is optional.
The reason for this is that the presence of the decimal point signals that the ones digit is a significant digit defining the precision of the number (when there are non-zero digits to the left of the decimal point).
Here, you're rounding to the ones place, and the result is a non-zero digit in that place, so the decimal point is optional.
_____
Comment on other rounding methods
The method described above will introduce a bias if many of numbers being rounded have a 5 that causes rounding up. In order to compensate, the method of "rounding to even" is suggested for such data sets. In that method, 8.5 would be rounded down to 8 (an even number), while 9.5 would be rounded up to 10 (an even number).
Generally, when rounding negative numbers, the sign is ignored by the rounding process, which proceeds as though the number were positive. Conventionally, -8.5 would be rounded to -9, for example.
_________
8.2 rounded to the nearest one is 8.
