Decimals: ordering, adding and multiplying

Place value after the point

In $3{,}47$ the $4$ is four tenths and the $7$ is seven hundredths. So $0{,}5$ is bigger than $0{,}45$, even though $45$ looks bigger than $5$: five tenths beats four tenths.

Ordering safely

Give every number the same number of decimal places by adding zeros: $0{,}5\to0{,}50$. Now compare digit by digit as with whole numbers. This one habit removes almost all ordering errors.

Adding and subtracting

Line up the decimal points, not the last digits. $12{,}4+3{,}75$ becomes $12{,}40+3{,}75=16{,}15$.

Multiplying by $10$ and $100$

The digits move left; the point stays put. $3{,}47\times10=34{,}7$. Saying “the digits move, not the point” keeps the idea straight when dividing too.