Calculating with decimals

1.99 euros for the cola, 0.75 litres in the bottle, 62.4 kg on the scales: as soon as things get more precise than whole numbers, the decimal point comes into play. If you can calculate with decimals confidently, you estimate prices in your head, scale recipes correctly, and notice immediately when a result can't be right. You already know how to add and subtract: write the numbers point under point, fill missing decimal places with zeros, and work place by place. This topic is mainly about multiplying and dividing, because there the point follows rules of its own.

Times 10 and divided by 10

A decimal number is nothing more than a place value chart with a point: to its left ones, tens, hundreds, to its right tenths, hundredths, thousandths. Times 10 makes every digit worth ten times as much, everything shifts one place to the left: the point moves one place to the right, and 3.7 becomes 37. Divided by 10 is the opposite: the point moves left, and 45.6 becomes 4.56. With times 100 or divided by 100 it moves two places.

Multiplying: without the point first

For 0.3 * 0.2, first calculate completely without the point: 3 * 2 = 6. Then count the decimal places of both numbers together: 0.3 has one, 0.2 has one, two in total. So the result gets two decimal places: 0.06. This always works, because 0.3 is 3 divided by 10 and 0.2 is 2 divided by 10, so the result must be divided by 100. Also check with an estimate: 0.3 * 0.2 is a small part of a small part, so the result must be well below 1.

Dividing: shift the point

For division there's a helpful trick: shift the point in both numbers by the same amount until the divisor is a whole number. 7.2 divided by 0.8 becomes 72 divided by 8 = 9, and the result stays the same because you multiplied both numbers by 10. That's exactly how you work out unit prices: if 0.75 litres of juice costs 1.50 euros, then 1 litre costs 1.50 divided by 0.75 = 150 divided by 75 = 2 euros.