Rational and Irrational Real Numbers Rational and Irrational

Let’s look at the relationships between number sets Let’s look at the relationships between number sets. Notice rational and irrational numbers make up the larger number set known as Real Numbers

A number represents the value or quantity of something… Like how much money you have.. Or how many marbles you have… Or how tall you are. As you may remember from earlier grades there are different types of numbers.

Here are the rational numbers represented on a number line.

Fractions and Decimals Rational Numbers Fractions and Decimals

Rational numbers – numbers that can be written in the form a/b (fractions), with integers for numerators and denominators. Integers and certain decimals are rational numbers because they can be written as fractions.

Remember you can simplify a fraction into a decimal by dividing the denominator into the numerator, or you can reduce a decimal by placing the decimal equivalent over the appropriate place value. O.625 = 625/1000 = 5/8

√2 = 1.414213562… no perfect squares here Irrational numbers √2 = 1.414213562… no perfect squares here

An irrational number cannot be expressed as a fraction. Irrational number – a number that cannot be expressed as a ratio of two integers (fraction) or as a repeating or terminating decimal. An irrational number cannot be expressed as a fraction. Irrational numbers cannot be represented as terminating or repeating decimals. Irrational numbers are non-terminating, non-repeating decimals.