Where it goes wrong
Traditional teaching
Decimals are taught as notation rules: line up the points, count the places, move the point when multiplying by ten. The deep continuity — that decimals are just place value extending rightward forever — is rarely made explicit, so 0.35 vs 0.5 becomes a guessing game.
The reteach
The Alice Method
Extend the place-value pattern the child already owns: each step right divides by ten — hundreds, tens, ones… so the pattern demands tenths, hundredths, thousandths. Zoom into the number line between 0 and 1 to find 0.3, then between 0.3 and 0.4 to find 0.35. Money makes it concrete; the zooming number line makes it precise.
Mental model
The infinite zoom
The number line is infinitely zoomable. Between any two marks there are ten more. A decimal is an address at some zoom level: 0.35 means 'zoom to the 0.3 neighborhood, then to house number 5.' Longer decimals aren't bigger numbers — they're finer addresses.
Transfer
Where this shows up for the rest of their life
Zooming between scales is how scientists and engineers think: kilometers to millimeters, billions to single users, years to milliseconds. Decimal fluency is really fluency at changing resolution without losing your place — the same skill as reading a map at two zoom levels.
Watch for these
Common misconceptions
The misconception
“Longer decimals are bigger: 0.35 > 0.5 because 35 > 5.”
The repair
This is whole-number thinking imported where it doesn't belong. On the zoomed number line, 0.5 sits visibly past 0.35. Money helps too: $0.50 beats $0.35.
The misconception
“'Move the decimal point' is what multiplying by 10 does.”
The repair
The digits shift to bigger place values; the point never moves. It sounds pedantic but the digit-shift picture is the one that survives contact with scientific notation later.
Seen, not said
The visual explanation
A number line that zooms: 0-to-1 divides into tenths, one tenth expands into hundredths. The child watches 0.35 get located, and 'decimal places' become physical locations instead of notation.
Try it
Interactive example
Watch one amount answer to three names — decimal, percent, fraction — as you slide it.
Percent, decimal, and fraction are one number wearing three outfits
Slide the shading. All three names update together — because they were never different things.
percent
30%
decimal
0.30
fraction
30/100
30% of 80 = 24