Place value to the right of the decimal point

Three of ten equal parts of a whole are 3/10, also written 0.3. The zero to the left of the decimal point means no complete ones; the 3 to the right counts three tenths.

Split each tenth into ten equal parts. The whole now contains one hundred pieces. One piece is 1/100; three are 0.03. The 3 in 0.3 and the 3 in 0.03 count different-size units.

The three tenth-rows in 0.3 contain thirty small cells. Thus 3/10=30/100 and 0.3=0.30. Appending zero did not create more; it expressed the same amount using smaller units.

Not every zero may be removed. Deleting the first zero after the decimal point in 0.03 gives 0.3, moving the 3 to a unit ten times larger. Distinguish trailing zeros from place-holding zeros.

1.25 combines one whole, two tenths and five hundredths. Put down one full hundred-grid and another twenty-five cells. Fractions and decimals are different ways of naming the same quantities.