Comparing decimals

Which is bigger, 6.456 or 6.465? You could mark both on a number line. Or compare place by place from the left, as with whole numbers:

So 6.465 is bigger.

The rule: start at the biggest place; while the digits are equal, move one place right; at the first place where they differ, the bigger digit wins.

Why can we stop there? The second number is ahead by a whole hundredth. All the thousandths and smaller places together can never add up to a whole hundredth, so they can't change the result.

Careful: more digits does not mean bigger with decimals. 0.1 is bigger than 0.009, even though 0.009 has more digits: 1 tenth beats 0 tenths. Try 1.23 vs 1.32, 3.81 vs 13.800, 1.009 vs 1.090.

Which of 0.9, 1.1, 1.01, 1.11 is closest to 1? In order: 0.9 < 1 < 1.01 < 1.1 < 1.11. The nearest on each side are 0.9 (10/100 away) and 1.01 (1/100 away). So 1.01 is closest. Try: which of 3.56, 3.65, 3.099 is closest to 4? Which of 0.8, 0.69, 1.08 is closest to 1?