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Yes. In fact, a number line would be full of an uncountably many infinite number of discontinuities (holes) without them and hence would not be a line, so in fact Irrational Numbers MUST be placed on the number line in order for it to exist.
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What is the meaning of the irrational number line?
There is no such thing as an irrational number line.
Can rational numbers be placed on the number line?
well every integer fraction whole number natural number are rational number's surely rational numbers are represented on a number line and as rational numbers are the real numbers
A real number that is not rational?
Real numbers are any numbers that could be on a number line. Rational numbers are numbers that can be expressed as fractions. Real irrational numbers are things like pi or the square root of 2.
In a short explanation what is the real number system?
Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers. The Real Numbers did not have a name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary.
Are irrational numbers cannot be represented on a number line?
Irrational numbers can be represented on a number line. For example, to graph the square root of two, draw a line of 1 unit (1 unit = the distance between the points of two whole numbers) from -1 which is perpendicular to the number line. Then, using a compass, place the pointy end on 0, the pencil tip on the end of the drawn line that is not touching the number line and drawing an arc so that it hits the number line on the positive side. Draw a point at where the arc meets the number line. That point is the square root of 2. This works because of Pythagoras theorem (a2+b2=c2, 12+12=22).
