Rounding Off Numbers and Significant Figures

Nowadays everyone have a calculator that helps to calculate large numbers, but large numbers are difficult to use in chemical tasks. So, it is very important to know how to round the answer off correctly.

We have two rules for rounding off numbers.

If the digit to be removed

is less than 5 (that is 1,2,3,4), the previous digit stays the same.

For example   2.334 the last digit is 4, which is less than 5, so the previous number 3 will stay the same. The answer is 2.33

           

            is equal to or greater than 5 (that is 5,6,7,8,9), the previous digit is increased by 1.

For example   2.336 the last digit is 6, which is greater than 5, so the previous number 3 will increase by 1. The answer is 2.34

Second part of my post is significant figures.

They are 3 rules that we have to understand to know how to count significant figures.

I.          Leading zeros are never significant.

For example

3 4 5 6 0 0 0 0 0, this number has 4 significant numbers (we don’t

        1   2  3  4                    count the zeros)

II.         Captive zeros are always significant numbers.

For example  

4 6 0 0 2 1, this number has 6 significant numbers

1  2   3  4   5  6                                 

III.       Trailing zeros are sometimes significant figures. This part makes some people confused. 

            I will try to explain this in very simple way.

            The trailing zeros are significant only if the number is written with a decimal point.

For example

3 4. 5 6 0 0 0  this number has 7 significant numbers because it has a decimal   

1   2   3  4   5  6  7   point between 4 and 5, which means the zeros are significant.

 Without the decimal point (3456000), we have only 4 significant numbers.

Now, let’s put all the information together by solving problems.

Round 53.7285 to four significant figures. The answer is 53.73 ( four s.f)

        

 This number has 6 significant figures, but they ask us to round the number to four significant figures. The fifth digit is 8, which is greater than 5(it is the second rule for rounding off numbers) so the previous number 2 will increase by 1, giving us 3.

Round 23.50343 to three significant figures. The answer is 23.5

           

This number has 7 significant figures, but they ask us to round the number to three significant figures. Look on the fourth digit, which is 0 less than 5, so the previous number 5 will stay the same (this is the first rule for rounding off numbers)