Significant Figures

Significant Figures are important to help find out which numbers are precise, and how to make number's more accurate. In every measurement, the last digit are usually uncertain. 

However, some quantities do not require you to round. For example, you cannot determine that there are 4.1 pairs of jeans, or 2.3 pencils.

There are some rules which you will have to remember in order to make the significant figures precise.

Keep in mind these rules on how to count significant figures:

1) Numbers that are greater than zero are ALWAYS counted as a sig dig. 

For example: 456793 . For this number here, there are 6 sig digs.

2) Zeros that come before a number>0 ARE NOT counted

For example: 0.000087 --> Although there are so many zeros before 87,  those zero's are not counted, therefore there are only 2 sig digs.

3) Zeros that go after the decimal points ARE counted


For example: 56.09  --> This number has 4 sig digs

4) Zeros that go after numbers>0, but ARE NOT before or after a decimal, ARE NOT counted

For example: 4120000000 --> This number has so many zeros, but there are only 3 sig digs

Go to this site for practice on counting sig figs, and see what you get! 

http://science.widener.edu/svb/tutorial/sigfigures.html 

Now on to rounding...

Memorize the following rules:

1) Look to the the number on the right of the digit in which you wish to round

2) If the number>5 round the number up

3) If the number<5 the number stays the same

4) If the number = 5 and there are number>0 after it, then round the number up

5) If the number IS 5 and ends in 5, make sure you round to make the last digit even, (0,2,4,6,8).

Here are some MATH RULES WHEN ADDING AND SUBTRACTING TO REMEMBER:

When you add or subtract you always look at the number that has the fewest number of decimal places, then you round the new number according to that.

For this equation you see that 1.6 has the fewest decimal places, so that means the new answer has to have only one decimal place as well. thus, instead of 23.934m, the answer is 23.9m

 
When you are multiplying or dividing, you find the number that has the fewest number of significant digits. Then you round by the fewest number of significant digits.

 

For more practice on rounding, adding, subtracting, multiplying, and dividing significant figures, visit this site:

 http://www.teacherbridge.org/public/bhs/teachers/Dana/SigFigOperations.html