Rounding numbers

We can round off numbers to the nearest thousand, nearest hundred, nearest ten, nearest whole number, or any other specified number. Because in most cases the accuracy is not very important.

For instance, if someone asks your weight you do not have to tell the most accurate number. Lets say you weight 71 kg and 345 grams. It would sound funny if you tell exactly this number. It sounds normal if you say, I am 71kg or approximately 70 kg. Or if anybody asks you how long have you been studying English, would you say 1 year 175 days and 5 hours? :) I believe you would say around one and half years instead.

So, we use rounding quite often, especially in everyday situations. Sometimes in maths exams it is asked to round the answer to some extend. Lets review 3 types of rounding

To the nearest ....

To round a number to some extend, we should know how exactly each digit is called. You may see it in the following picture

Rounding to the nearerst thousand means, 3 digits should be kept after the decimal point. To the nearest hundredth means 2 digits should be left after roundins; to the nearest tenth means 1 digit should be left after the point etc.
While cancelling the unnecessary digits, you round up if the first number is 5 or more and round down if the first digit less than 5

Lets round the number 3628.1749
-to the nearest thousandth => 3628.175
-to the nearest hundredth => 3628.17
-to the nearest tenth => 3628.2
-to the nearest whole number => 3628
-to the nearest ten => 3630
-to the nearest hundred => 3600
-to the nearest thousand => 4000

More examples:

You may also watch a video rounding

To 1 decimal place, 2 decimal places etc...

This is similar to the above reviewed task.
Rounding to 1 decimal place is the same as rounding to the neareast tenth
Rounding to 2 decimal place is the same as rounding to the nearest hundredth
3 decimal places is the same as to the nearest thousandth etc

Rounding to several significant figures.....

Another consideration in rounding is when you are required to round to "an appropriate number of significant digits". What are significant digits? Well, they're sort of the "interesting" or "important" digits. 

With the number 368249, the 3 is the most significant digit, because it tells us that the number is 3 hundred thousand and something. It follows that the 6 is the next most significant, and so on.

When a number starts with 0, the zeros at the beginning are not count. With the number 0.0000058763, the 5 is the most significant digit, because it tells us that the number is 5 millionths and something. The 8 is the next most significant, and so on.

Be careful however with numbers such as 30245, the 3 is the first significant figure and 0 the second, because of its value as a place holder.

Lets round the number 3628.1749
-to 7 s.f. => 3628.175
-to 6 s.f => 3628.17
-to 5 s.f => 3628.2
-to 4 s.f => 3628
-to 3 s.f => 3630
-to 2 s.f. => 3600
-to 1 s.f => 4000

If you still find it difficult, then the following video may be useful

Now, lets check if you have understood. Try the following exercises and check your answers below

We hope it helps. If you like it, please share with friends.

You may also find a revision note on changing the subject of a formula here

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