Is .6 a rational number?

Question

Levi Adams · Accepted Answer

A rational number is a number that can be expressed as a ratio of two integers; since it is an integer ratio, it can have both positive and negative values. Further, any decimal fraction, which limits itself beyond the decimal point (such as #5.7# which does not go beyond tenth place) or has continuously repeats numbers (till infinity) beyond a certain place of decimal (such as #4.33333....# or #0.232142857142857142857....#) can be easily written as ratio of integers, however large and hence are rational. Now as #0.6=6/10#, is a ratio of two integers, it is a rational number.

Mila Anderson · Answer

#0.6" is a rational number"#

The basic rule is whether it meets one of two requirements.

#color(blue)("Condition 1")# Is it a terminating decimal?

Example: 0.125 It ends because it stops after the 5.

#color(white)(.)#

#color(blue)("Condition 2")# Is it a repeating decimal

For instance, 0.356356356356.

written as #0.356bar356# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(olive)("If the decimal satisfies either of these 2 conditions then, yes.")# #color(olive)("A rational number is a number that can be written in the form of a fraction")#

#color(magenta)("By the way the counting numbers are rational")#

#color(magenta)(1/1"; "2/1"; "3/1"; "4/1...."& so on")# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(red)("Answering your question")#

#0.6 =6/10# as this can be written as a fraction it is a rational number.

Autumn Arnold · Answer

undefined Yes, 0.6 is a rational number because it can be expressed as the fraction 6/10, which can be simplified to 3/5. Rational numbers are those that can be expressed as the quotient of two integers, where the denominator is not zero.