Decimals

Prices like 2.49 €, a running time of 12.8 seconds, a height of 1.75 m: you come across decimals every day. They are nothing more than a very handy way of writing fractions, and with a little place value intuition you calculate with them just as confidently as with whole numbers.

The places continue after the point

Left of the decimal point you already know the places: ones, tens, hundreds. Right of the point the pattern continues, only each place becomes ten times smaller: first the tenths, then the hundredths. So 3.47 has 3 ones, 4 tenths and 7 hundredths. The point simply marks the border between wholes and parts.

Decimals are fractions in disguise

Every decimal is a fraction with 10, 100, 1000 and so on in the denominator. 0.5 means 5 tenths, that is 5/10, simplified 1/2. 0.25 means 25 hundredths, that is 25/100, simplified 1/4. Whenever a decimal feels strange, translate it into a fraction: you will often see immediately what it means.

Comparing, adding and subtracting

Is 0.3 bigger than 0.25? Yes, because 0.3 is 30 hundredths and 0.25 only 25. Mentally attach zeros until both numbers have the same number of decimal places, then you can compare them directly. Written addition uses the same idea: line the numbers up so the decimal points sit under each other. Then add place by place as usual, and the point lands in the same position in the result. You do this already when paying: 2.49 € and 1.15 € make 3.64 € together. Subtracting works the same way: point under point, fill missing decimal places with zeros, and take away place by place. A 4 becomes 4.00 that way, and 4.00 − 1.15 gives 2.85.