A longer decimal is not a bigger one
Which is bigger, 0.35 or 0.4? 0.35 has more digits, and 35 is bigger than 4, so 0.35 can look bigger. But a digit is worth what its place says, not what the digits after it look like.
0.4 is 4 tenths. 0.35 is 3 tenths and 5 hundredths. Compare the tenths first: 3 tenths is less than 4 tenths, so 0.35 is less than 0.4, and the hundredths do not change that. The 5 hundredths are not even one more tenth.
Give them the same number of places
A zero at the end of a decimal adds nothing: 0.4 and 0.40 are the same number, 4 tenths and no hundredths. Write 0.4 as 0.40, and both numbers count hundredths. 35 hundredths is less than 40 hundredths, so 0.35 < 0.40.
Money makes it easy to see. $0.40 is 40 cents and $0.35 is 35 cents, and 40 cents is more.
The bright gold cells are 0.35: 3 full rows and 5 more. The pale cells carry on to 0.40, which is 4 full rows. 0.35 stops short of 0.40.
Inside the tenth
On a number line, 0.35 lies between 0.3 and 0.4, inside the tenth that ends at 0.4. Every number in that tenth, 0.31, 0.35 or 0.39, is less than 0.4, however large its last digit is.
the tenth from 0.3 to 0.4 holds ten hundredths, and every number inside it is < 0.4, however large its last digit looks: 0.32 = 32/100 < 40/100
Find 0.35 between 0.3 and 0.4
The tenth from 0.3 to 0.4 is drawn again underneath, cut into ten hundredths. Move the marker to 0.35: it stays inside the tenth, short of 0.40.
Place by place
To compare any two decimals, compare the whole-number parts first. If they are equal, compare the tenths, then the hundredths, then the thousandths. The first place where the digits differ decides.
For 2.09 and 2.1, the whole parts are both 2, and the tenths are 0 and 1, so 2.1 is bigger. For 0.7 and 0.76, the tenths are both 7. Write 0.7 as 0.70: 0 hundredths is less than 6 hundredths, so 0.76 is bigger. The shorter number was bigger the first time and smaller the second, so the number of digits never decides.
When every place matches, the numbers are equal: 0.5 and 0.50 are the same number.
From 0.6 to 0.8 in hundredths. 0.7 and 0.76 both have 7 tenths, and 0.76 has 6 hundredths more, so it lies 6 steps past 0.7.