Thousandths

Cut each hundredth into ten again. That gives thousandths, the third place after the point.

Reading it aloud

0.325 is read "three hundred twenty-five thousandths". The last place names the whole thing.

Expanded form

0.325 is 0.3 + 0.02 + 0.005, or 3/10 + 2/100 + 5/1000.

Where "and" goes

In 4.6 the word "and" marks the point: "four and six tenths".

One more cut

Split each hundredth into ten and you have thousandths. Three decimal places means thousandths: 0.472 is 4 tenths, 7 hundredths and 2 thousandths — or 472 thousandths altogether. Both readings describe the same number and each is useful in different situations.

Reading them correctly

0.472 is "four hundred seventy-two thousandths". The place name comes from the last digit, since that is the smallest unit present. Saying it in full keeps the fractional meaning alive and makes comparisons much easier to reason about.

Where thousandths appear

A millimetre is a thousandth of a metre. Engineering tolerances, medicine doses and athletics times all use three decimal places routinely — an Olympic sprint can be decided by 0.003 of a second. The precision is not academic.

The fraction underneath

0.472 is 472/1000. Every terminating decimal is a fraction whose denominator is a power of ten, which is exactly why decimals and fractions can always be converted between. Seeing the fraction makes the size of a small decimal much easier to judge.