Why 1/3 is 0.333...

0:00Why is one third equal to 0.333, with threes that never stop?

0:07The fraction bar means divide, so one third is 1 divided by 3.

0:153 does not go into 1, so write 0 on top.

0:19Write 1 as 1.000, which is worth the same, and put the point straight above.

0:273 goes into 10 three times, because 3 times 3 is 9.

0:33Subtract 9 from 10, and 1 is left over.

0:38Bring down the next 0, and we have 10 again.

0:41So 3 goes into 10 three times again, and 1 is left again.

0:48Bring down another 0, and the very same thing happens.

0:54The remainder is always 1, so we always get back to 10.

1:00That means the threes go on forever, and the division never ends.

1:06We write three dots to show that the threes keep going.

1:10A decimal with digits that repeat forever is called a repeating decimal.

1:15We can also show this by putting a bar over the 3.

1:19One third is 0.333 repeating, because 1 divided by 3 always leaves 1.