Decimal Place Value Zoom

Pre-Algebra · Axiom Academy

Zoom into a number line, gap by gap, and watch decimals reveal smaller and smaller parts of a whole. What lives between two whole numbers? A plain number line only shows whole numbers — 0, 1, 2, all the way up. But the world is full of in-between amounts: 5.4 miles, 3.79, a 0.002-inch gap. Decimals are how we name those points, and the trick is simple: keep zooming in. Watch the line zoom into the tiny gap where the number 5.372 hides. Each time you magnify a gap by 10, ten new evenly-spaced marks appear — and one more digit of the number snaps into place. Every zoom slices one gap into 10 equal pieces — that is exactly what the next decimal place counts. Trapping 5.372, one tenth at a time Slide the dial to zoom deeper. At each level the current gap is split into 10 equal parts, and the number falls into exactly one of them — that choice is the next digit. Drag down to whole numbers, up to thousandths, and watch the digits build: 5, then 5.3, then 5.37, then 5.372. Each level pins the number 10 times tighter — a gap one-tenth as wide as the one before. Step right of the point: every place is one-tenth the last The digits you trapped each sit in a named place. Drag across the places to the right of the decimal point. Moving one step right always makes a place worth one-tenth as much: the ones, then tenths (1/10), then hundredths (1/100), then thousandths (1/1000). The bars shrink by a factor of 10 every step.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.