Comparing Decimals

Write both to the same number of places, then compare like whole numbers.

Start from the left

Tenths outrank hundredths. 0.4 beats 0.39 because 4 tenths beats 3 tenths.

Length does not decide

0.5 is longer written as 0.50, but it never changes size. Do not judge by digits.

Compare from the left, place by place

To compare 0.45 and 0.5, look at the tenths first: 4 against 5. Five tenths beats four tenths, so 0.5 is larger. As with whole numbers, the leftmost difference settles it and nothing further right can change the outcome.

Pad with zeros to make it obvious

Write 0.5 as 0.50 and the comparison with 0.45 becomes 50 hundredths against 45 hundredths. Padding puts both numbers in the same unit, which is the same fix used for comparing fractions with unlike denominators.

The longer-looks-bigger trap

Many people say 0.45 is bigger than 0.5 because it has more digits. It is not. Always compare place by place, or pad and compare as whole counts. This error is so common that catching yourself making it is a real achievement.

Check on the number line

Place both on a line split into tenths, with the tenths further split into hundredths where needed. The one further right is bigger. When a decimal comparison feels uncertain, the line settles it and builds the intuition for next time.