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To round a number you must first find the rounding digit, or the digit occupying the place value you're rounding to. Then look at the digit to the right of the rounding digit. If it is less than 5, then leave the rounding digit unchanged. If it is more than five, add one to the rounding digit. If it is five, the rule is to always round up (add one to the rounding digit). This rule was created to "break the tie" when you are rounding a number that is exactly between two other numbers. These kinds of rules are called "conventions", and are important so we all get the same answer when doing the same problems.
If you're dealing with a decimal number, drop all of the digits following the rounding digit.
If you're dealing with a whole number, all the digits to the right of the rounding digit become zero.
This sounds a lot more complicated than it really is!
It's easiest to learn rounding by studying examples.
To round
the number 16,745.2583
to the nearest thousandth
First find the rounding digit. This is the "8".
You are trying to get rid of the all the digits to the right of the 8, but
you want the result to be as accurate as possible.
Now look one digit to the right, at the digit in the tenthousandths place which is "3". See that 3 is less than 5, so leave the number "8" as is, and drop the digits to the right of 8. This gives 16,745.258.
To round
14,769.3352 to the
nearest hundred
Find the rounding digit, "7".
Look at the digit one place to right, "6".
Six is more than 5, so this number needs to be rounded up. Add one the rounding
digit and change all the rest of the digits to the right of it to zero. You
can remove the decimal part of the number too. The result is 14,800.
To round
365 to the nearest
ten
Find the rounding digit, "6". Look
at the digit to the right of the six, "5".
Since 365 is exactly halfway between 360 and 370, the two nearest multiples
of ten, we need the rule to decide which way to round. The rule says you round
up, so the answer is 370.
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