To round numbers off, find the digit in the position you’re interested in, and look
at the next digit (the one to the right).
If that digit on the right is less than five, round down (which means leave your digit alone).
If the digit on the right is five or more, round up (which means you have to increase
your digit by one).
Let’s look at some examples.
Whole numbers first.
Round three hundred and forty-two to the nearest ten.
First, find at the digit in the tens column: the four.
Look at the digit on the right: it’s a two.
That’s less than five, so we’ll round down: leave the four as is.
Three hundred and forty.
Round two point three nine eight to the nearest whole.
First, find the digit position that represents a whole number: that’s easy, it’s just
to the left of the decimal point.
Now, look at the digit on the right: it’s three.
That’s less than five, so round down: leave the two as it is.
The nearest whole number to two point three nine eight is two.
Notice that it doesn’t matter that the next two digits are both bigger than five.
It doesn’t matter what they are.
You only need to look at the one digit to the right of where you’re rounding.
Nothing else.
Round twenty-eight point seven one to the nearest whole.
Find the whole number digit: to the left of the decimal point.
Look at the next digit on the right: a seven.
That’s more than five, so round up: The eight has to round up to nine.
Twenty-nine.
Again, the one after the seven makes no difference here.
Only the single digit on the right of where you’re rounding matters.
You don’t need to look any further.
Okay, so let’s go futher into the decimals.
Round two point six nine to the nearest tenth.
Well, the process is exactly the same.
Find the digit that represents tenths: that’s the six.
Look at the next digit on the right: a nine.
More than five, so round the six up to seven.
Two point seven.
Round twelve point zero five to the nearest tenth.
Again, find the digit for the tenths: that’s the zero.
Look at the next digit on the right: it’s five.
That’s five or more, so we have to round up: round the zero to one.
Twelve point one.
Getting the hang of this?
Round zero point one eight two six to the nearest hundredth.
Well, the digit for the hundredths is the eight.
The digit to the right is a two, so round down: Zero point one eight.
Again, any extra digits to the right don’t affect the outcome.
A couple more interesting cases and then we’re done.
Round zero point four three nine six to the nearest thousandth.
Well, where’s the digit for thousandths?
It’s the nine.
The next digit on the right is a six, so we have to round up.
But if I round nine up, I get ten: the nine becomes a zero, and I carry a one to the left:
which means I also have to round the three up to four.
So my rounded answer is zero point four four zero.
See what happened there?
This process can go further, too.
Try this one: Round twenty-nine point nine six to the nearest tenth.
Here’s the tenths digit, and the digit on the right is six, so we have to round up.
Nine becomes zero, carry one.
The next digit is also a nine, so round it up: zero, carry one.
The two rounds up to three, and our rounded answer is thirty point zero, to the nearest
tenth.
Two questions for you to think about, to help you make sure you really understand what rounding
is about.
Why don’t you have to look any further to the right?
Why is it that those extra digits on the right don’t change the result?
And, why is it that if the digit on the right is five, you round up and not down?