Mathematics Rules:

Scientific Notation:

1.    number must be 1 n < 10

2.    if you move decimal left, exponent increases

3.    if you move decimal right, exponent decreases

4.    adding or subtracting, exponents must be the same

5.    multiplying, exponents are added

6.    dividing, exponents are subtracted

7.    watch negative exponents carefully

8.    converting to scientific notation does not affect significant digits

9.    don't bother using 101, 100, 10-1

 

Significant Figures:

1.    all non-zero digits are significant

2.    zeros between other digits are significant

3.    trailing zeros to the right of the decimal are significant [0.30]

4.    zeros to the right of the decimal that are used to space to the decimal are not significant (i.e. 0.0030 [2 sig. figs.])

5.    zeros to the left of the decimal are not significant unless the decimal point is present (i.e. 12000 [2 sig. figs.] but 12000. [5 sig. figs.])

6.    line over a zero indicates last significant digit (the estimated digit)

7.    adding and subtracting, answer can only have as many decimal places as the least precise measurement

8.    multiplying and dividing, answer will be rounded to the same number of significant digits as the measurement with the smallest number of significant figures

9.    you must estimate one digit beyond that of the graduations on the measuring device

10.                      if you are rounding a terminal five, round up if the preceding digit is odd, drop the five if the preceding digit is even

11.                      exact numbers or counters are not considered when determining how many significant digits an answer should have

12.                      keep one extra significant digit if you are going to perform more calculations with an answer