1/3 times 3 is really 1 ?

Assume you have 3 empty plates 1 whole cake. If you divide the cake into 3 parts and each part then each plate contains 1/3 part of the cake, that is:
= 1/3
Of course, 1/3 is 1/3 and not 0.333333...infinite.

If now you want to see how many cakes are there in the plates all you have to do is to multiply the parts, 1/3 each, by 3 which is the number of the plates, thus:
= 1/3 * 3
= 3/3 or 1

Assuming you don't remember how many cakes did you divide into 3 equal parts but you know that you placed each part to 6 plates then you will still know how many cakes were that by the same procedure we did above, you divided each by 3 and therefore each part is 1/3, and you placed each part to 6 plates then:
= 1/3 * 6
= 6/3 or 2

Now, you know that there were two cakes which you divided 3 parts each and placed each part to 6 plates.

But remember, 1/3 is 1/3 and 0.33333... is 0.33333, in the same way that 2/3 is not 0.66666666...infinite or 0.66666667, a figure which was already rounded, else you'll to 0.33333 or 0.66666 infinitely without stop.

(1/3) x 3 = 3/3 = 1

Similarly :-
1/2 x 2 = 1
1/4 x 4 = 1
1/5 x 5 = 1
"
"
"
1/200 x 200 = 1

etc etc

1/3 x 3
= 3/3
= 1

Because if you multiply the fractions, it makes one.
1/3 x 3/1
So that becomes 3/3 which equals 1.

Because 1/3 cannot be divided perfectly, so it is best to leave it as a fraction when multiplying it:
(1/3)X3=3/3=1

If you put that problem into a more advanced calculator, it will give you 1 instead of .9999999999.....

Simple.
who said 1/3 times 3 is not 1
The number of digits that the caculator can show is limited.
It cannot show infinitely large number of digits.
What it can show is only approximate.

as 1/3 x 3 =3/3 (3 one-thirds)
3/3 =1

(1/3) times 3 makes 1
(1/3) * (3/1) = 3/3
3/3 = 1

1/3 x 3 = 1

same as
1/3 x 3/1 = 1
3/3 = 1

!/3, as a fraction, will give a recurring decimal when 3 is divded into onto 1.