Significant Digits : Significant Digits They’re not so bad
How do I know what is significant? : How do I know what is significant? *There are some simple rules to follow to determine what digits in a number are significant.
*Rule 1: Any real digit 1-9 is considered significant.
How to deal with zeros : How to deal with zeros *Rule 2: The zeros are the hard part:
*If a zero is between two real digits it counts.
203- has three significant digits
*If a zero is at the end of a number we must look to see if there is a decimal point.
Rule 2 continued : Rule 2 continued Ex. 2330 has three significant digits
2330. has four significant digits
*The reason for that is because the decimal point indicates that we are certain of that final zero. Therefore, it would count as significant.
Rule 2 continued : Rule 2 continued * If the number is a decimal and the zero comes before the number it is not significant, they act as placeholders (they push the digits to the proper spot).
0.0045 has two significant digits
*If the number is a decimal and
the zero comes after the number it is significant, it shows us certainty.
0.00450 has three significant digits
When and how to use significant digits : When and how to use significant digits * Anytime that you write a number from a measurement you must think about how certain you are of your measurement and only estimate one place farther than your tool can measure.
Ex. This ruler measures in cm with mm in between so we would measure 7 cm 8 mm and since the line is in between the 8 and 9 we estimate 5 giving us 7.85cm.
When and how to use significant digits continued : When and how to use significant digits continued *If you are working a problem with specific values your answer needs to be rounded off to the proper number of significant digits.
*Your answer cannot be more certain than your least certain measurement (think: a chain is only as strong as its weakest link).
Practicing Significant Digits : Practicing Significant Digits *So, let’s look at an example:
345 + 2.04 + 16.00 + .05 = 363.09
*First we must determine how many digits each number in our problem has.
345 has 3, 2.04 has 3, 16.00 has 4 and .05 has 1.
*The number with the smallest number of significant digits tells us how many digits to round to, so in this case we need to round to 1.
That means that our answer would become 400
For Further Practice : For Further Practice *The following website has practice problems available for you to try. The more you practice the easier this skill becomes.
http://science.widener.edu/svb/tutorial/sigfigures.html