Number Line

Page 1

Number Line

N - The Natural numbers. This is the set of positive whole numbers i.e. 1,2,3,4,5…..etc

Z – The Integers. This is the set of negative and positive whole numbers which includes 0 i.e. …-3,-2,-1,0,1,2,3…

R – The Real Numbers. This consists of all the numbers on the number line

Q – The set of rational numbers. This is any number that can be expressed as a fraction.

Numbers that are not rational are irrational and are denoted R\Q. Irrationals cannot be expressed as fractions. Irrationals have an infinite amount of decimal places. A good example of this is π.

Since π = 3.14159… etc it has an infinite amount of decimal places, it is irrational

Another good example is a root such as or. They cannot be expressed as fractions and have an infinite amount of decimal places, therefore they are irrational.

Take x to be any number

If x N then x is a Natural number If x Q then x is a Rational number

If x Z then x is an Integer If x R then x is a Real number

If x R\Q then x is Irrational

4.1

Give two reasons why − 7·3 is not a natural number.

1. It’s not positive

2. It’s not a whole number

4.2

Why is 7.41 not an irrational number.

It can be expressed as a fraction so it is a rational number.

Since it is rational it cannot be irrational

4.3

Under what sets of numbers does zero comes under?

0 is not a Natural number. The natural numbers start at 1 i.e 1,2,3,4,5…

0 is an Integer

0 is Rational as it can expressed as

0 is Rational so it is not Irrational

0 is Real as it is on the number line

4.4

State which set of numbers (Natural numbers, Integers etc… ) the following numbers come under , 8, 3.5, - 4 ,

- Not Natural, Not an Integer, Not Rational, Real and Irrational R, R\Q

It is on the number line and it has an infinite amount of decimal places

8 – Natural, Integer, Rational, Real, Not Irrational N, Z, Q, R

Whole number that’s positive and on the number line

3.5 – Not Natural, Not an Integer, Rational, Real and Not Irrational Q, R

Not a whole number, can be expressed as a fraction and is on the number line

-4 - Not Natural, Integer, Rational, Real and Not Irrational Z, Q, R

Negative whole number, can be expressed as a fraction and is on the number line

- Not Natural, Not an Integer, Not Rational, Real and Irrational R, R\Q

It is on the number line and it has an infinite amount of decimal places

4.5

State which set of numbers (Natural numbers, Integers etc… ) the following numbers come under -8 , , 6, ,

-8 - Not Natural, Integer, Rational, Real and Not Irrational Z, Q, R

Negative whole number, can be expressed as a fraction and is on the number line

- Not Natural, Not an Integer, Rational, Real and Not Irrational Q, R

Not a whole number, can be expressed as a fraction and is on the number line

6 – Natural, Integer, Rational, Real, Not Irrational N, Z, Q, R

Whole number that’s positive and on the number line

– Not Natural, Not an Integer, Not Rational, Real and Irrational R, R\Q

It is on the number line and it has an infinite amount of decimal places

- Not Natural, Not an Integer, Not Rational, Real and Irrational R, R\Q

It is on the number line and it has an infinite a