2 Intro to Mathematics
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Transcript of 2 Intro to Mathematics
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INTRODUCTION
TO MATHEMATICS
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Introduction
Transformation of science was
made in the 17th century when it
was learned that it can be
expressed mathematically
Ideas expressed in numbers are
said to be unambiguous.
It does not give double meanings.
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Introduction
Findings expressed mathematically
are easier to verify or to disprove
by experiment.
The use of mathematics gave way
to the enormous success of science.
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SIGNIFICANT FIGURES
It is the number of reliably known
digits a numerical quantity
contains.
For measured quantity, usually it is
all the digits that can be read
directly from the instrument used
in making the measurement.
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RULES: NON-ZERO
All non-zero digits are always
significant.
Ex. 1, 2, 3, 4, 5, 6, 7, 8, & 9
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RULES: The Digit Zero
Zeros may not be significant,
depending on whether they mark
the decimal point or indicate a
measured value.
Leading Zeros
Confined Zeros
Trailing Zeros
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RULES: LEADING ZERO
Zeros located at the beginning of a
number are NEVER significant.
They merely locate the decimal
point.
Ex.: 0.0897 3 SF
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RULES: CAPTIVE ZERO
Zeros located between non-zero
digits are ALWAYS significant.
Ex.: 2805.3 5 SF
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RULES: TRAILING ZERO
Zeros located at the end of a
number ARE SIGNIFICANT ONLY if
the number has an EXPLICITLY
SHOWN DECIMAL.
Ex.: 123.00 5 SF
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RULES: TRAILING ZERO
In WHOLE NUMBERS WITHOUT A
DECIMAL POINT that end in one or
more zeros, the zeros may NOT BE
SIGNIFICANT.
Ex.: 3900 2 SF
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RULES: TRAILING ZERO
Numbers expressed in scientific
notation with zero, follows the rule
in decimal number.
Ex.: 3.0 x 102 2 SF
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EXERCISES
1. 25.25
2. 200.5
3. 0.0025
4. 0.025
5. 300
6. 0.00500600701007. 5.890 x 105
8. 0.00234 x 10-4
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ROUNDING OFF
NUMBERS
If the next digit after the last
significant figure is 5 or greater,
round up.
Increase the last significant figure
by 1.
Example: 2.136 becomes 2.14
rounded to 3 SF
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ROUNDING OFF
NUMBERS
If the next digit after the last
significant figure is less than 5,
round down.
Do not change the last significant
figure.
Example: 2.132 becomes 2.13
rounded to 3 SF
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EXERCISES
1. 5679
2. 986.981
3. 0.087624. 0.0123
5. 45.81
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Significant Figures in
Calculations
For addition and subtraction:
Round off the sum or difference
based on the least number of digits
after the decimal point.
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Significant Figures in
Calculations
For multiplication and division:
Round off the product or quotient
based on the number that contains
the least number of SF.
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SCIENTIFIC NOTATIONS
It is a shortcut way of expressing
very large and small numbers.
Numbers are expressed into
greater than but less than ten with
a power of ten.
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RULES: Scientific Notation
To express a number greater than 1
in scientific notation, we count the
number of places the decimal point
has to be moved to the left to putjust after the first digit of the
number.
The number of movement ofdecimal point equals the positive
exponent.
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EXAMPLE
30,000,000
can be expressed as3 x 107
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RULES: Scientific Notation
To express a number smaller than 1
in scientific notation, we count the
number of places the decimal point
should be placed after the firstnon-zero digit.
The number of movement of
decimal point to the right equalsthe negative exponent.
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EXAMPLE
0.0008
can be expressed as
8 x 10-4
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EXERCISES
1. 7,020,000
2. 847
3. 0.0004624. 0.00000184
5. 72.4
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RULES:
Multiplication and Division
In multiplication, the numerical
parts are simply multiplied
together and the exponents are
added.
In division, the numbers are
divided and the exponents are
subtracted algebraically.
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EXAMPLE
(2 x 103) (2 x 102)
= (2 x 2) x (103+2)
= 4 x 105
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RULES:
Addition and Subtraction
In adding or subtracting numbers
in scientific notation, the exponents
must be the same number
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EXAMPLE
(2.5 x 102) + (1.20 x 102)
= (2.5 + 1.20) x (102)
= 3.7 x 102
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EXAMPLE
(2.5 x 102) + (1.20 x 103)
= (2.5 x 102) + (12.0 x 102)
= 14.5 x 102