To discover the number of irrational numbers between 1 and 6 as well as bonus information about irrational numbers, simply continue reading.
How many irrational numbers are between 1 and 6?
You may be surprised to learn that there are infinite irrational numbers between 1 and 6. A surprising fact as most individuals assume that there would be a finite, definitive amount of irrational numbers between two numbers which are seemingly close together.
Why are there countless irrational numbers between 1 and 6? Remember what irrational numbers are. Irrational numbers are numbers which can’t be expressed with whole fractions which feature two whole numbers a denominator and a numerator. Common examples of irrational numbers include numbers which have infinite numbers after their decimal point.
A great example of an irrational number, which features infinite unique numbers after its decimal point is pi. Pi’s first 10 digits are 3.1415926535. As you can imagine, pi is just one example of the infinite irrational numbers between the whole numbers 1 and 6. Hopefully this simple example, illustrates how its possible that there are infinite irrational numbers between two seemingly small numbers.
So remember that while there are infinite irrational numbers between two numbers that have a larger gap such as 1 and 1,000,000, there are also infinite irrational numbers between numbers that are closer together such as 1 and 6 and 1 and 4.
Interesting facts about irrational numbers:
1. Numbers with decimal points can in fact be rational numbers
While numbers with decimal points are often irrational numbers, such as pi, be careful when it comes to defining numbers which feature decimal points as numbers with decimal points can be rational numbers. As an example, the number9.5. Remember that rational numbers can be expressed as whole fractions. Taking the above example 9.5 can be expressed as a simple fraction, 19/2. Both the denominator and the numerator in this fraction are whole numbers, which is also a requirement of fractions which can be made from rational numbers
.Another example of a decimal number, which may at first look like an irrational number, is the number .001. To see whether .001 happens to be a rational digit, you need to turn it into a fraction which features whole numbers. Expressed as a whole fraction the digit .001 can be written as 1/1000. As you’ll notice both the numerator and the denominator are whole numbers, which confirms that the example above is a rational number, even though it has a smaller value than the number 1.2.
There are a few famous examples of irrational numbers While you already know that the number pi is an irrational number, there are also other examples of famous irrational numbers. As an example, the golden ratio is another example of a famous irrational number and the first few numbers of the golden ratio are 1.61803398874948482.
If you’ve never heard of the golden ratio, the golden ratio is a special number which is commonly used in art, geometry and architecture. Hopefully you now have a greater understanding of irrational numbers and how to identify irrational numbers as well as rational numbers.