Comparing Decimals

Which is bigger, 0.5 or 0.45? Many people say 0.45, because 45 is bigger than 5. But 0.5 is 5 tenths, while 0.45 is only 4 tenths and 5 hundredths. Five tenths is more, so 0.5 is the bigger number.

The safe method is to line up the decimal points and compare place by place from the left. Write 0.5 as 0.50 so both numbers have two places, then set it against 0.45. The tenths decide it, 5 against 4, and the hundredths never get a say.

Adding zeros at the end of a decimal never changes its value: 0.50 is 5 tenths and 0 hundredths, the same amount as 0.5. That is what makes the comparison fair, since both numbers are now counted in hundredths, 50 against 45. On the number line 0.5 lies to the right of 0.45, so 0.5 > 0.45.