Can rational and irrational numbers be negative?

Question

Autumn Arnold · Accepted Answer

Yes

Yes, rational and irrational numbers can be negative. Te only thing that is desired is that they could be mapped to a place on a real number line. Negative numbers are to the left of #0# on number line. By definition, rational numbers are a ratio of two integers #p# and #q#, where #q# is not equal to #0#. Hence, if #p# is negative and #q# is positive (or vice versa but #q!=0#), #p/q# could be negative. Examples of negative rational numbers are #-3.14159#, #-17/4#, #-2/3# or #-3.bar(142857)# (here #bar(142857)# indicates these numbers are repeating infinitely). These are equivalent to #-314159/100000#, #-17/4#, #-2/3# or #-22/7# (in form #p/q#). Similarly there could be negative irrational numbers too like #-pi#, #root(3)(-80)#, #-sqrt2# etc. These are equivalent to their positive irrational numbers like #pi#, #root(3)(80)#, #sqrt2# but towards left of #0# on real number line. Similarly, there could be irrational numbers like #6-3pi# which are #3pi# units to the left of #6#, but as this would lie to the left of #0#. Some other such numbers are #1-sqrt3#, #root(3)2-sqrt5#, #-sqrt17+2# and #-7.239135113355111333555.....#. (The last number is non-terminating non-repeating decimal number and hence an irrational number.)

Roman Alvarez · Answer

undefined Yes, both rational and irrational numbers can be negative. Rational numbers are any numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. These numbers can be positive, negative, or zero. For example, -1/2, -3, and -5/4 are all rational numbers.

Similarly, irrational numbers are numbers that cannot be expressed as a simple fraction of two integers. These numbers also include negative values. For instance, -√2, -π, and -e are examples of irrational numbers that are negative. Therefore, both rational and irrational numbers can have negative values.