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Rounding Numbers (page 1 of 3)

Sections: General rounding, Rounding and significant digits

When you have to round an answer, you are usually told how much to round it. It's simplest when you're told how many "places" to round to, but you should also know how to round to a named "place", such as "to the nearest thousandth" or "to the ten-thousandths place". You may also need to know how to round to a certain number of significant digits.

Let's use the first few digits of pi: 3.14159265...

• Round pi to five places.

First, I count out five decimal places, and then look at the sixth place:

3.14159 | 265...

I've drawn a little line separating the fifth place from the sixth place. This is often handy, especially if you are dealing with lots of digits. The fifth place has a 9 in it. Looking at the sixth place, I see that it has a 2 in it. Since 2 is less than five, I won't round the 9 up; that is, I'll leave it alone. Then pi, rounded to five digits, is:

3.14159

• Round pi to four places.

First, I go back to the original number (not the one I just rounded), count off four places, and look at the number in the fifth place:

3.1415 | 9265...

The number in the fifth place is a 9, which is greater than 5, so I'll round up in the fourth place. That is, the 5 becomes a 6, and pi, rounded to four decimal places, is:

3.1416

• Round pi to three places.

First, I go back to the original number (not the one I just rounded), count off three places, and look at the number in the fourth place:

3.141 | 59265...

The number in the fourth place is a 5, which is the cut-off for rounding: if the number in the next place (after the one you're rounding to) is 5 or greater, you round up. In this case, the 1 becomes a 2, and pi, rounded to three decimal places, is:

3.142

This rounding works the same way when they tell you to round to a certain place. The only difference is that you have to be a bit more careful in counting off the places you need. Just remember that the decimal places count off to the right in the same order as the counting numbers count off to the left. That is, for regular numbers, you have the place values:

...(ten-thousands) (thousands) (hundreds) (tens) (ones)

For decimal places, you don't have a "oneths", but you do have the other fractions:

(decimal point) (tenths) (hundredths) (thousandths) (ten-thousandths)...

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• Round pi to the nearest thousandth.

That means that I need to count off three decimal places, and round:

3.141 | 59265...

Then pi, rounded to the nearest thousandth, is 3.142.

• Round 2.796 to the hundredths place.

The hundredths place is two decimal places, so I'll count off two decimal places, and round according to the third decimal place:

2.79 | 6

Since the third decimal place contains a 6, which is greater than 5, I have to round up. But rounding up a 9 gives a 10. In this case, I round the 79 up to an 80:

2.80

You might be tempted to write this as "2.8", but, since you rounded to the hundredths place (to two decimal places), you should write both decimal places. Otherwise, it looks like you rounded to one decimal place, or to the tenths place, and your answer could be counted off as being incorrect.

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