Is the number 1 rational or irrational?

Question

Autumn Arnold · Accepted Answer

Rational

A rational number is one that can be expressed as a fraction of integers. For instance, we can express the number 1 in an infinite number of ways: #1/1, 2/2, 3/3, (-1)/(-1)# In fact, any integer divided by itself will give us 1. An irrational number is one that cannot be expressed as a fraction of two integers. For instance, the most famous of irrational numbers is #pi# - the ratio of a circle's circumference to its diameter. As an approximation, #pi# is sometimes expressed as #3.14# or #22/7#, but in actuality the decimal runs forever, never repeating and never ending.

Aurora Arias · Answer

The number 1 can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer.

This is only possible because #1# is a RATIONAL number.

Once a number is irrational, that's it. It cannot be classified further. However,#color(magenta)(" rational")# numbers can be classified into different types of numbers. A rational number is defined as 'A number which can be written in the form #color(magenta)(p/q)# where #p and q# are integers, but #q !=0# Some rational numbers become integers, some remain as fractions: Integers:#30/5, 12/4, -9/3, color(magenta)(7/7), 0/8# Fractions: #2/3, 15/4, 1/7# Some integers are negative, the rest are whole numbers. Whole numbers include #{0,color(magenta)(1),2,3,4,5,6,......}# Whole numbers can be broken down into 0 and natural numbers. Natural numbers include #{color(magenta)(1)(,2,3,4,5,6...}# Within the natural numbers you will also have different types of numbers, including odds, evens, primes, composites, perfect squares, perfect cubes, etc. The number #color(magenta)(1)# can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer. This is only possible because it is a rational number. Note that #color(magenta)(1)# is not prime because it has only one factor.

Riley Anderson · Answer

undefined The number 1 is a rational number.