Rounding Numbers

What is "Rounding" ?
Rounding means reducing the digits in a number while trying to keep its value similar. The result is less accurate, but easier to use.

Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.


Common Method

There are several different methods for rounding, but here we will only look at the common method, the one used by most people ...
How to Round Numbers

* Decide which is the last digit to keep
* Leave it the same if the next digit is less than 5 (this is called rounding down)
* But increase it by 1 if the next digit is 5 or more (this is called rounding up)

Example: Round 74 to the nearest 10

* We want to keep the "7" as it is in the 10s position
* The next digit is "4" which is less than 5, so no change is needed to "7"

Answer: 70

(74 gets "rounded down")
Example: Round 86 to the nearest 10

* We want to keep the "8"
* The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9"

Answer: 90

(86 gets "rounded up")

So: when the first digit removed is 5 or more, increase the last digit remaining by 1.
Why does 5 go up ?

5 is in the middle ... so we could go up or down. But we need a method that everyone can agree to always use.

So think about sport: you should have the same number of players on each team, right?


* 0,1,2,3 and 4 are on team "down"
* 5,6,7,8 and 9 are on team "up"

And that is the most important part of the "common" method of rounding. It is not a perfect method, but it is the one most people use.
Rounding Decimals
First you need to know if you are rounding to tenths, or hundredths, etc. Or maybe to "so many decimal places". That tells you how much of the number will be left when you finish.


Examples Because ...
3.1416 rounded to hundredths is 3.14 ... the next digit (1) is less than 5
1.2635 rounded to tenths is 1.3 ... the next digit (6) is 5 or more
1.2635 rounded to 3 decimal places is 1.264 ... the next digit (5) is 5 or more
Rounding Whole Numbers

You may want to round to tens, hundreds, etc, In this case you replace the removed digits with zero.
Examples Because ...
134.9 rounded to tens is 130 ... the next digit (4) is less than 5
12,690 rounded to thousands is 13,000 ... the next digit (6) is 5 or more
1.239 rounded to units is 1 ... the next digit (2) is less than 5
Rounding to Significant Digits

To round "so many" significant digits, just count digits from left to right, and then round off from there.

Note: if there are leading zeros (such as 0.006), don't count them because they are only there to show how small the number is.
Examples Because ...
1.239 rounded to 3 significant digits is 1.24 ... the next digit (9) is 5 or more
134.9 rounded to 1 significant digit is 100 ... the next digit (3) is less than 5
0.0165 rounded to 2 significant digits is 0.017 ... the next digit (5) is 5 or more

Significant Digit Calculator

(Try increasing or decreasing the number of significant digits. Also try numbers with lots of zeros in front of them like 0.00314, 0.0000314 etc)