Significant Figures

Hello how are you doing?

Ready to learn more new stuff about chemistry.

We are going to teach you about "Significant Figures" or for a lack of a better expression: How to write you math answers correctly.

I know that right now you people are going to be like "Why are we learning math?", "Isn't this physics or something?" and yapping about how this isn't chemistry.

This part is about units and writing them properly.

Significant Figures are not very big or small numbers, it is MEANINGFUL NUMBERS

There are some rules that you need to know:

• Last digit of a number is uncertain
• That number can be either one digit higher or lower

Eg: Take 2.56g ; numbers 2 and 5 are certain however 6 is uncertain therefore it can either be one digit higher(7) or lower(5)

• Significant Figures  includes all certain digits plus one uncertain digits

There are some exceptions

• Leading zeros DON'T count (eg. 0.01 has 1 sig. digit because 0.0 are leading zeros)
• Trailing Zeros COUNT (eg. 10.050 has 5 sig digits because 0 after 5 is trailing and 0's before 1 and 5 are between certain numbers)
• Trailing zeros without decimal point DON'T count (eg. 12000 has 2 sig. digit because 0's after 12 is not stopped by a decimal)

NOTE:

Some quantities are exact meaning no decimal mubers

Eg. pair of shoes are always 2 shoes

       1 dog not 0.75 dog

       1m = 100cm

These numbers are decided so think carefully.

                                                                                  

Rounding:

Rounding numbers are basically the same as what you would do in math class

However with one set of EXCEPTIONS:

1. Look at the digit after the number you have to round
2. If that digit is greater than 5, round up
3. If that digit is less than 5, keep the same
4. If that digit is equal to 5 and there are more digits after, round up
5. If that digit is equal to 5 and it ends at the 5, make the last number even (eg. 0,2,4,6,8) 

                                                                          

Adding, Subtracting, Multiplying and Dividing:

When adding or subtracting round to the fewest number of decimal places

Eg.  12.544g
       + 1.3g    
         13.844g

In this case you have to round to 1 decimal place because 1.3 has fewer number of decimals than 12.544 so the answer becomes 13. 8g

Eg.  12500mL
       + 6000mL
         18500mL

In this case, you have to round to the thousands because that is fewer digits than 12500 so the answer becomes 18000mL 

When multiplying or dividing, round to the fewest number of significant digits:

Eg.  12.54m
       x  1.3 m
        3762
    +12540
       16.302square meters

In this case, you should round the answer so that there are 2 significant digits so the answer becomes 16meters squared

                            9.646m
Eg.   1.3m |  12.54m
                      117      
                           84
                           78
                             60
                             52
                               8

In this case, the answer is 9.6m because 1.3 has 2 sig. digits and 12.54 has 4 sig digits.

REMEMBER:

Always use the rule: round to the fewest sig. figs for multiplying and dividing

Thank you for tuning in. We will see you next time

Ciao!

Written by JK (Oct 27,2010)