More digits does not mean more number. Walk the places left to right, stop at the first difference.
1Walk Left to Right
Ones
Tenths
Hundredths
Thousandths
3
.
2
4
6
3
.
2
5
0
same
same
4 < 5
Both hold 3 ones and 2 tenths. Hundredths differs first, and 4 is less than 5, so 3.246 < 3.25. Nothing to the right can overturn it.
2Longer Is Not Larger
0.45 > 0.6
✗ 45 beats 6
0.45 < 0.60
✓ 45 vs 60 hundredths
Counting digits is a whole number habit. 0.45 is forty-five hundredths and 0.6 is sixty hundredths, so the longer number is the smaller one.
3End Zeros, Inside Zeros
0.6 = 0.60 = 0.600
same value, more places
0.45
45 hundredths
0.045
45 thousandths
A zero after the last digit fills an empty place and changes nothing. A zero right after the point shoves every digit one place further right, so 0.045 is a tenth of 0.45.
4Order Them on a Line
0.45 < 0.504 < 0.6
A line settles a whole set, and puts 0.504 just past 0.5. The symbol opens toward the larger number.
