Download Significant Figures - Waterford Public Schools

Significant Figures &
Scientific Notation
 Measurements
are important in science
(particularly chemistry!)
 Quantity that contains both a number and a
unit
 Must be able to say how “correct” a
measurement is

No measurement is perfect and exact!
2
types:
 Exact
The amount of money in your
account
 Known with certainty

 Approximate

Weight, height
 Anything MEASURED
 No measurement is perfect!
ALL measurements have some amount of
uncertainty or error
 All certain digits and the first uncertain digit in a
measurement are considered significant
 Example:



A ruler can measure to the nearest 0.1 centimeter
Ruler also allows estimation between each 0.1 cm
division
A
measurement between 40.1 cm and 40.2
cm is estimated at 40.16 cm
 The estimate has 4 significant figures


3 digits are certain
1 digit is uncertain

Five basic rules

All non-zero digits are significant


Zeros appearing between non-zero digits are significant


Example: 0.0025
Zeros in a decimal occurring after the first non-zero digit
are always significant


Example: 1.008
Zeros in a decimal occurring before the first non-zero
digit are not significant


Example: 1457
Example: 4.2079
Exact numbers (numbers obtained by counting or from
definitions) are assumed to have unlimited number of
significant figures

Never limits the number of significant figures in a calculation



Place the number in an outline of the United States
If decimal point is PRESENT, begin counting with the
first non-zero digit from the PACIFIC side of the USA
If a decimal point is ABSENT, begin counting the first
non-zero digit from the ATLANTIC side of the USA
Pacific
(Decimal Present)
Atlantic
(Decimal Absent)
 25
cm
 305 cm
 0.00123 in
 400 g
 400. m
 0.94600 mL
 12 in = 1 ft
2
3
3
1
3
5
Exact number so
infinite # of sig figs

Addition and subtraction




Solution must have the same number of decimal places
as the least accurate number
i.e. Solution is rounded to the least number of decimal
places in the data
Solution with correct number of significant figures:
2540.
Be sure to LINE UP DECIMAL POINT when
adding/subtracting
 Multiplication




and division
Solution must have the same number of
significant digits as the least accurate number
i.e Solution is rounded to the least number of
significant figures in the data
4.8069 must be rounded to 2 significant figures
4.8069 becomes 4.8
 Rounding


Carry all digits significant or extra through all
steps in the calculation. Only the final value is
rounded to the correct number of significant
figures.
To round, look at the digit following the one to
be rounded. If it is 5 or more, round up; if it is
less than 5, round down.
 In
chemistry (and all sciences), the SI system
of units is used for all measurements
 In
the metric system, prefixes are used to
modify base units
 Convert
2.3 cm to m

Numbers like 12,000 or 546 are written in
standard form

Scientific notation makes it easier to work with
very large or very small numbers

It is based on the power of ten and written as:

N x 10z



N is the number and z is the exponent
Example: 7.65 x 10-3
The exponent that the base ten is raised to
shows the number of places left or right that the
decimal place needs to be moved

Proper use includes:

A number with only one digit to the left of the decimal
point and as many as needed to the right

A number between
 Example: 2.3456



and
1 digit to the left of the decimal point
4 digits to the right of the decimal point
Number ten (10) raised to an exponent



The exponent is the number of “place holders” needed to
change the number from a conventional number to a number
with only one digit to the left of the decimal point
If the decimal point is moved to the left (number greater than
1), the exponent will be a positive number
 Example:
If the decimal point is moved to the right (number less than 1),
the exponent will be a negative number
 Example:
 Convert
notation










each standard number into scientific
2.78 x 106
9.34 x 102
7.32 x 105
2.78 x 108
9.34 x 10-2
1.6 x 103
7.3 x 10-5
1.6 x 10-3
9.34 x 104
7.32 x 10-5

Addition and subtraction



Convert each number so that they all have the same
exponent
Add or subtract the numbers
The exponents for each base number 10 will not change


If the answer does not have just one digit to the left of
the decimal point, convert the answer to the correct
scientific notation



Put the given exponent on the “10”
If you move the decimal to the right, add -1 to the exponent
If you move the decimal to the left, add +1 to the exponent
General formulas:
 Multiplication

Multiply the base numbers normally and then add
the exponents together
 Division

Divide the base numbers normally and then
subtract the exponents
 General
formulas:
Have fun measuring
and happy calculating!