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Pre Algebra 23 - Scientific Notation - v.2
Scientific notation allows us to more easily express very large or very small numbers encountered in engineering and science. Using exponents, we can convert standard decimal numbers into scientific notation and vice versa.
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Pre-Algebra 09 - Division and Prime Numbers
The building blocks of all natural numbers are the prime numbers. The early Greeks invented the system still used today for separating natural numbers into prime and composite numbers.
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Pre-Algebra 03 - Decimal, Binary, Octal & Hexadecimal
Our modern decimal number system is base-10. Other number systems used in fields like computer engineering are base-2 (binary), base-8 (octal) and base-16 (hexadecimal).
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Pre-Algebra 04 - Whole Numbers, Integers, and the Number Line
Number systems evolved from the natural "counting" numbers, to whole numbers (with the addition of zero), to integers (with the addition of negative numbers), and beyond. These number systems are easily understood using the number line.
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Pre-Algebra 13 - Reciprocals and Division With Fractions
When working with fractions, division can be converted to multiplication by the divisor's reciprocal. This chapter explains why.
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Pre-Algebra 17 - Improper Fractions and Mixed Numbers
Sometimes arithmetic operations result in fractions greater than one, called "improper" fractions. An improper fraction can be converted into a "mixed number" composed of an integer plus a "proper" fraction.
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Pre-Algebra 25 - Simplifying Divided Exponential Expressions
Exponential expressions with divided terms can be simplified using the rules for subtracting exponents.
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Pre-Algebra 18 - Converting Fractions to Decimal Numbers
Any fraction can be converted into an equivalent decimal number with a sequence of digits after the decimal point, which either repeats or terminates. The reason can be understood by close examination of the number line.
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Pre-Algebra 15 - Least Common Denominators
Sometimes when finding a common denominator we create an unnecessarily large common denominator. This chapter explains how to find the smallest possible common denominator.
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Pre-Algebra 22 - Exponents of One, Zero, and Negative
Integer exponents greater than one represent the number of copies of the base which are multiplied together. But what if the exponent is one, zero or negative? Using the rules of adding and subtracting exponents, we can see what the...
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Pre-Algebra 31 - Simplifying Radical Expressions
Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign.
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Pre-Algebra 06 - Commutative Property of Multiplication
The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.
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Pre-Algebra 24 - Simplifying Multiplied Exponential Expressions
Exponential expressions with multiplied terms can be simplified using the rules for adding exponents.
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Pre-Algebra 19 - Converting Terminating Decimal Numbers to Fractions
Decimal numbers with a finite number of digits after the decimal point can be easily converted into fractions. This chapter explains why.
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Pre-Algebra 07 - Associative and Distributive Properties of Multiplication
A look at the logic behind the associative and distributive properties of multiplication.
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Pre-Algebra 30 - Rational Exponents
Exponents can not only be integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers.
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Pre-Algebra 01 - The Dawn of Numbers
A humorous look at early attempts at creating number systems, leading up to our modern base-10 decimal number system which uses "positional notation". The story takes place on the fictitious island of Cocoloco.
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Pre-Algebra 33 - Real Numbers
There are an infinite number of rational numbers, but there are infinitely more irrational numbers. Neither type of number can represent every type of numeric quantity. By combining the rational and irrational numbers into the real...
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Pre-Algebra 05 - Commutative & Associative Properties of addition
A look behind the fundamental properties of the most basic arithmetic operation, addition.
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Pre-Algebra 16 - Reducing Fractions
The process of reducing any fraction to its simplest possible form is easily visualized using the number line.
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Pre-Algebra 02 - Roman Numerals, Sign-Value vs Positional Notation
Roman numerals are an ancient base-10 natural number system. Understanding Roman numerals (a sign-value notation) can shed light on our modern number system which uses positional notation.
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Pre-Algebra 11 - Fractions and Rational Numbers
The first fractions used by ancient civilizations were "unit fractions". Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational...
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Pre-Algebra 20 - Converting Repeating Decimal Numbers to Fractions
Decimal numbers with an infinitely repeating sequence of digits after the decimal point can be converted into fractions. This chapter explains why.
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Pre-Algebra 08 - Multiplying Negative Numbers
When number systems were expanded to include negative numbers, rules had to be formulated so that multiplication would be consistent regardless of the sign of the operands.
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