"Comparing decimals. Decimal fractions (decimals for short — the numbers to the right of the decimal point) are a notoriously challenging topic in the elementary math curriculum." Just to point out this is the most ass backwards way to talk about decimal fractions I have ever witnessed, but nothing would stop said Valerie Strauss on pedagogical insufficiency spotting... "decimals for short — the numbers to the right…
"Decimals" is (in the US at least) a common way of referring to decimal fractions (that is, numbers represented like: 12.345) vs the whole number or integer representation that the students would already be familiar with (like 12) or other fractional notations like 6 7/10.