Transcript Scientific Notation

Math Outline
Math Concepts Important to Chemistry
A.
B.
C.
Significant Figures and Rounding
Scientific Notation
Unit Conversions & Conversion Factors
A. Significant Figures
• A measurement always has some degree of uncertainty.
• Different people estimate differently.
• Record all certain numbers and one estimated number.
A. Significant Figures
• Some numbers are exact; others are not.
– Exact numbers can be counted or defined.
i.e.-the no. of people in the class, eggs in a dozen
– Numbers from measurements are not exact.
i.e.-volume of 53.5 mL…
• Significant digits are used to demonstrate what was
actually counted in a measurement and to what degree
it was estimated.
(includes all measured + 1 estimated digits)
• All non-zero numbers you see in a recorded
measurement are significant.
Significant Figures: the tricky parts…
There are several rules to tell if a zero is significant:
1. All zeroes between non-zero numbers ARE
significant.
2. Zeroes used to position the decimal ARE NOT
significant.
3. Zeroes to the right of numerical digits AND to the
right of a decimal ARE significant.
4. Use scientific notation OR a decimal to eliminate
confusion about multiple zeroes at the end of a
number.
1.
Sumup
Nonzero integers always count as significant figures.
1457
4 significant figures
2. Zeros
a. Leading zeros - never significant
0.0025
2 significant figures
b. Captive zeros - always significant
1.008
4 significant figures
a. Trailing zeros - significant only if the number is written
with a decimal point
100
1 significant figure
100.
3 significant figures
120.0 4 significant figures
3. Exact numbers - unlimited significant figures
• Not obtained by measurement
• Determined by counting OR Determined by definition
3 apples
1 in. = 2.54 cm
Math and Significant Figures
The first thing to remember:
…the answer in your calculator
is NOT “THE ANSWER!”
The Rounding Rules
• Sometimes you have to round in order to have a
desired number of significant figures:
• If the last significant digit place is followed by a
number less than 5 ……………… LEAVE IT!
(fill with placeholders as needed)
• If the last significant digit place is followed by a 5
or a number greater than 5 ………… ROUND UP!
(fill with placeholders as needed)
Practice Rounding
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456,500 (round to 2 sig figs) = _________________
76,822 (round to 2 sig figs) = _________________
9,985 (round to 3 sig figs) = _________________
125,475 (round to 5 sig figs) = _________________
90,044 (round to 2 sig figs) = _________________
45,988,335 (round to 4 sig figs) = _______________
449,589 (round to 4 sig figs) = _________________
120,045 (round to 3 sig figs) = _________________
26,645 (round to 4 sig figs) = _________________
980 (round to 1 sig fig)
= _________________
Math and Significant Figures
In multiplication and division:
• The answer must contain no more significant
figures than the LEAST number of significant
figures used in the problem.
Math and Significant Figures
In addition and subtraction:
• When reading left to right, the last digit of the
answer is in the same position of the FIRST
ESTIMATED digit used in the problem.
B. Scientific Notation
Changing a standard number into sci. not.:
• Move the decimal to the place after the first non-zero
number. (Count places; that will be the exponent.)
• If you are moving the decimal to the left, your exponent
will be positive. (Every space the decimal moves to the left, the
exponent increases by one)
34, 500  3.45 x 104
• If you are moving the decimal to the right, your
exponent will be negative. (Every space the decimal moves to
the right, the exponent decreases by one)
0.00761 7.61 x 10-3
Scientific Notation (cont’d)
Changing sci. not. number into standard:
1. If the exponent is positive, move the decimal to
the right (make the number “bigger”) and fill
with zeros:
3.67 x 104  36,700
2. If the exponent is negative, move the decimal to
the left (make the number “smaller”) and fill
with zeros:
5.908 x 10-2  0.05908
Math Operations with Scientific Notation
Multiplication:
1. Multiply the base numbers
2. Add the exponents
3. Adjust to correct scientific notation format
Division:
1. Divide the base numbers
2. Subtract the exponents
3. Adjust to correct scientific notation format
More Math with Scientific Notation
Addition and Subtraction:
1. Change the members of the problem so
that they all have the same exponent.
2. Add or subtract the base numbers.
3. DO NOT CHANGE THE EXPONENT!
4. Adjust to correct scientific notation
format.