The decimal form of 1/3 is a repeating decimal. Are all the multiples of 1/3 also repeating decimals? Explain.

Answer 1

3 times 1/3 is 1 which is not a repeating decimal,

Unless you consider 3 x 0.333... = 0.9999.... as repeating, but 0.999..... = 1.000

It's an unusual argument, but true.

Let x= 1/3 = 0.333....

then 3x = 0.9999....

but x=1/3 also means 3x = 1, just multiply both sides by 3

and if x = 0.333... then 3(0.333...) = 1 = 0.999....

there's only an "epsilon" difference which = 0, 1/infinity = 0