# Real Numbers

-Real Numbers are every number.

-Therefore, any number that you can find on the number line. -Real Numbers have two categories, rational and irrational.

Rational Numbers

-Any number that can be expressed as a repeating or terminating decimal is classified as a rational number Examples of Rational Numbers

6 is a rational number because it can be expressed as 6.0 and therefore it is a terminating decimal. -7 ½ is a rational number because it can be expressed as -7.5 which is a terminating decimal. Examples of Rational Numbers

Square root 25 is a rational number because it can be expressed as 5 or 5.0 and therefore it is a terminating decimal. 2.45 is a rational number because it is a repeating decimal. Irrational Numbers

-An irrational number is a number that cannot be written as a fraction of two integers. -Irrational numbers written as decimals are non-terminating and non-repeating. Note: if a whole number is not a perfect square, then its square root is an irrational number. Caution!

A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Examples of Irrational Numbers

Square root of 21 is an irrational number because it can Not be expressed as a terminating decimal. 0.62622622262222… is an irrational number because it cannot be expressed as a repeating decimal. Examples of Irrational Numbers

Π (pi)is an irrational number.

Subsets of Rational Numbers

-Natural numbers

-Whole numbers

-Integers

Natural Numbers

Natural Numbers are counting numbers from {1,2,3,4,5,…}

Whole Numbers

Whole numbers are counting numbers from {0,1,2,3,4,5,…}

Integers

Integers include the negative counting numbers: {…,-3,-2,-1,0,1,2,3…} What Does It Mean?

-The number line goes on forever.

-Every point on the line is a Real number.

-There are no gaps on the number line.

-Between the integers there are countless other numbers. Some of them are rational (fractions, terminating and repeating...

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