Download Significant Figures and Scientific Notation

Significant Figures and Scientific Notation
Significant Figures – all the digits that can be known precisely in a measurement,
plus one digit that is estimated.
Why are significant figures important?
Indicates the precision of the measurement.
Rules for determining whether a digit is significant:
1. Every non zero digit in a reported measurement is significant
Example: 45.3 meters
(3 significant figures)
2. Zeros appearing between nonzero digits are significant
Example: 30045 (5 significant figures)
3. Leftmost zeros appearing in front of nonzero digits are not significant
Example: 0.0071 (2 significant figures)
4. Zeros at the end of a number and to the right of a decimal point are
always significant
Example: 43.00 (4 significant figures)
5. Zeros at the rightmost end of a measurement that lie to the left of an
understood decimal point are not significant if they serve a placeholders to
show the magnitude of the number
Example: 8000 meters (1 significant figure)
6. There are 2 situations in which numbers have an unlimited number of
significant figures
1. Counting
Example: 23 people (Unlimited significant figures)
2. Involves exactly defined quantities such as those found within a
system of measurement
Example: 60 min = 1 hour
Determining significant figures when adding and subtraction
The answer to an addition or subtraction calculation should be
rounded to the same number of decimal places as the measurement
with least number of decimal places.
Example: Calculate the sum of the three measurements
12.52 meters + 349.0 meters + 8.24 meters
Since 349.0 has the fewest decimal places you answer must be rounded
to one decimal place.
12.52 meters + 349.0 meters + 8.24 meters = 369.8 meters
Determining Significant figures when multiplying or dividing
The answer to a multiplication or division calculation should be
rounded to the same number of significant figures as the
measurement with the least amount of significant figures.
Example: 7.55 meters x 0.34 meters
Since 0.34 has the fewest significant figures, your answer must only
have 2 significant figures.
7.55 meters x 0.34 meters = 2.6 meters2
Scientific Notation – a given number is written as the product of two numbers: a
coefficient and 10 raised to a power.
Example. 602,000,000,000,000,000,000,000 = 6.02 x 10-23
Avogadro’s Number = Number of representative particles
contained in one mole of a substance
Adding and subtraction using scientific notation:
To add or subtract numbers expressed in scientific notation the exponents
must be the same. Once the exponents are the same you add or subtract the
coefficients and keep the exponents the same.
Example: (8.0 x 102) + (5.4 x 103)
You must first change the exponents so they are the same. To do that, move
the decimal one to the left on the quantity 8.0 x 102 so the quantity is now
0.80 x 103. Now add the coefficients together and keep the exponents
(.80 x 103) + (5.4 x 103) = 6.2 x 103
Multiplication and Division using scientific notation:
To multiply or divide numbers expressed in scientific notation you multiply
the coefficients and add the exponents, or divide the coefficients and subtract
the exponents.
Example: (3 x 104) + (2 x 102) = 6 x 106
Example: (4 x 105)/(2 x 102) = 2 x 103