Significant Figures --- By Sally Chen

Significant Figures
1. A bunch of certain digits and only one uncertain digit (at the end)


Exact Numbers
1. A certain amount
2. No rounding is required
3. Has infinite number of sig figs (eg. 1 pen = 1.000.....00 pen)


Significant Figures Rules
1. Non-zero digits are always significant 
2. Zeroes between two non-zero numbers are significant 
3. Zeroes at the beginning of a number are never significant 
4. Zeroes that fall at the end of a number and after decimal point are always significant
5. Zeroes at the end are AMBIGUOUS. They are not considered significant, unless there is a decimal that follows it.


Practise: 
How many sig. figs in the following numbers?
a. 500.0
b. 500
c. 0.05
d. 5.00x10^3


Adding / Subtracting with Significant Numbers
1. Perform the operation as usual 
2. Round to the smallest of digits past the decimal in any terms.

Multiplying / Dividing with Significant Numbers
1.Perform the operation as usual 
2.Round to the smallest number of significant digits in any operand.

Rounding when it comes to 5

Look at the digit after the position of rounding:

{IF}  > 5,  {THEN} round up!
{IF}  < 5, {THEN} keep the same!
{IF}  = 5 with digits after 5, {THEN} round up!
{IF}  = 5 without digits after 5,  {THEN} round to the nearest even number!

DO NOT ROUND UNTIL THE FINAL ANSWER!!