# ABE Math Tutorials/Whole numbers/Rounding

## ROUNDING

 Whole numbers

If you are sent out to buy 4 cups of coffee, at 99¢ per cup, how do you figure out how much money you need to take? Chances are, you think to yourself: "Ninety-nine cents is almost a dollar. For 4 cups of coffee, I'm going to need almost 4 dollars". This process, of figuring out costs to the nearest "round" number, is called rounding.

Of course, it's not just in dollars and cents that we use rounding. There are many real-life situations where we have to come up with "round numbers". For example, if you are looking for a meeting place for a group of people, it usually doesn't matter whether you will have exactly 82 or 83 people there. All that matters is that you know that you'll have about 80 people attending. In this case, you have rounded the number to the nearest ten.

What if you had 88 people coming? In this case, you would need a meeting place for about 90 people; because 88 is actually closer to 90 than it is to 80. But what if 85 people were attending? The number "85" is exactly half-way between 80 and 90. When you have to round off a "5", the usual practice is to round the number up.

Let's look at a few more examples in the following table:

 Number Rounded Becomes Why 41 to the nearest ten 40 41 is closer to 40 than it is to 50 29 to the nearest ten 30 29 is closer to 30 than it is to 20 65 to the nearest ten 70 when you round the number "5", you always round up 98 to the nearest ten 100 98 is closer to 100 than it is to 90

Let's look at the number 462. If we round this number to the nearest ten, we will round it to 460 (because 462 is closer to 460 than it is to 470). But what if we need to round it to the nearest hundred? In this case, we look instead to the digit that is in the hundreds place in this number (remember place value?). In this case, there is a "4" in the hundreds place. 462 is between 400 and 500. Is it closer to 400, or closer to 500? We know that 450 would be exactly half-way between 400 and 500: 462 is actually more than half-way. So 462 is closer to 500. We can say that 462, rounded to the nearest hundred, becomes 500.

Ready to try a few rounding questions?

1. 46, rounded to the nearest ten
2. 128, rounded to the nearest ten
3. 695, rounded to the nearest hundred
4. 249, rounded to the nearest hundred
5. 249, rounded to the nearest ten
6. 95, rounded to the nearest hundred
7. 891, rounded to the nearest ten
8. 250, rounded to the nearest hundred

1. 50; because 46 is closer to 50 than it is to 40
2. 130; because 128 is closer to 130 than it is to 120
3. 700; because 695 is closer to 700 than it is to 600
4. 200; because 249 is closer to 200 (but just barely!) than it is to 300
5. 250; because 249 is closer to 250 than it is to 240
6. 100; because 95 is closer to one hundred than it is to no hundreds (ie. zero)
7. 890; because 891 is closer to 890 than it is to 900
8. 300; because even though 250 is exactly half-way between 200 and 300, when the number we are rounding (the "50" part of it) starts with a "5", we round up.

It is a fairly easy procedure to round small numbers to the nearest ten or the nearest hundred. But when we have to round larger numbers, we need a more general procedure for rounding. Let's look at an example:

round 446,139 to the nearest thousand

Since we have to round to the nearest thousand, we first have to see which digit is in the thousands' place. It might help to put the number in a place value table, like we did before: